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RD Sharma solutions for Class 10 Mathematics chapter 5 - Arithmetic Progression

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RD Sharma 10 Mathematics

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Chapter 5: Arithmetic Progression

Ex. 5.10Ex. 5.20Ex. 5.30Ex. 5.40Ex. 5.50Ex. 5.60Others

Chapter 5: Arithmetic Progression Exercise 5.10 solutions [Page 5]

Ex. 5.10 | Q 1.1 | Page 5

Write the first three terms in each of the sequences defined by the following

an = 3n + 2

Ex. 5.10 | Q 1.1 | Page 5

Write the first three terms in each of the sequences defined by the following

an = 3n + 2

Ex. 5.10 | Q 1.2 | Page 5

Write the first five terms of the following sequences whose nth term are

`a_n = (n - 3)/3`

Ex. 5.10 | Q 1.3 | Page 5

Write the first five terms of the following sequences whose nth terms are:

`a_n = 3^n`

Ex. 5.10 | Q 1.4 | Page 5

Write the first five terms of the following sequences whose nth terms are:

`a_n = (3n - 2)/5`

Ex. 5.10 | Q 1.5 | Page 5

Write the first five terms of the following sequences whose nth terms are:

an = (−1)n 2n

Ex. 5.10 | Q 1.6 | Page 5

Write the first five terms of the following sequences whose nth terms are:

`a_n = (n(n - 2))/2`

Ex. 5.10 | Q 1.7 | Page 5

Write the first five terms of the following sequences whose nth terms are:

an = n2 − n + 1

Ex. 5.10 | Q 1.8 | Page 5

Write the first five terms of the following sequences whose nth terms are:

an = 2n2 − 3n + 1

Ex. 5.10 | Q 1.9 | Page 5

Write the first five terms of the following sequences whose nth terms are:

`a_n = (2n - 3)/6`

Ex. 5.10 | Q 2.1 | Page 5

Find the indicated terms in the following sequences whose nth terms are:

an = 5n - 4; a12 and a15

Ex. 5.10 | Q 2.2 | Page 5

Find the indicated terms in each of the following sequences whose nth terms are:

`a_n = (3n - 2)/(4n + 5)`; `a_7 and a_8`

Ex. 5.10 | Q 2.3 | Page 5

Find the indicated terms in each of the following sequences whose nth terms are

an = n (n −1) (n − 2); a5 and a8

Ex. 5.10 | Q 2.4 | Page 5

Find the indicated terms in the following sequences whose nth terms are:

an = (n − 1) (2 − n) (3 + n); a1, a2, a3

Ex. 5.10 | Q 2.5 | Page 5

Find the indicated terms of the following sequences whose nth terms are:

`a_n = (-1)^2 n; a_3, a_5, a_8`

Ex. 5.10 | Q 3.1 | Page 5

Find the next five terms of the following sequences given by:

`a_1 = a_2 = 2, a_n = a_(n - 1) - 3, n > 2`

Ex. 5.10 | Q 3.2 | Page 5

Find the next five terms of the following sequences given by

a1 = a2 = 2, an = an−1 − 3, n > 2

Ex. 5.10 | Q 3.3 | Page 5

Find the next five terms of the following sequences given by:

`a_1 = -1, a_n = (a_n - 1)/n, n>= 2`

Ex. 5.10 | Q 3.4 | Page 5

Find the next five terms of the following sequences given by:

a1 = 4, an = 4an−1 + 3, n > 1.

Chapter 5: Arithmetic Progression Exercise 5.20 solutions [Pages 8 - 9]

Ex. 5.20 | Q 1 | Page 8

Show that the sequence defined by an = 5n −7 is an A.P, find its common difference.

Ex. 5.20 | Q 1 | Page 8

Show that the sequence defined by an = 5n −7 is an A.P, find its common difference.

Ex. 5.20 | Q 2 | Page 8

Show that the sequence defined by an = 3n2 − 5 is not an A.P

Ex. 5.20 | Q 2 | Page 8

Show that the sequence defined by an = 3n2 − 5 is not an A.P

Ex. 5.20 | Q 3 | Page 8

The general term of a sequence is given by an = −4n + 15. Is the sequence an A.P.? If so, find its 15th term and the common difference.

Ex. 5.20 | Q 3 | Page 8

The general term of a sequence is given by an = −4n + 15. Is the sequence an A.P.? If so, find its 15th term and the common difference.

Ex. 5.20 | Q 4.1 | Page 8

Write the sequence with nth term:

an = 3 + 4n

Ex. 5.20 | Q 4.1 | Page 8

Write the sequence with nth term:

an = 3 + 4n

Ex. 5.20 | Q 4.2 | Page 8

Write the sequence with nth term an = 5 + 2n

Ex. 5.20 | Q 4.2 | Page 8

Write the sequence with nth term an = 5 + 2n

Ex. 5.20 | Q 4.3 | Page 8

Write the sequence with nth term an = 6 − n

Ex. 5.20 | Q 4.3 | Page 8

Write the sequence with nth term an = 6 − n

Ex. 5.20 | Q 4.4 | Page 8

Write the sequence with nth term: an = 9 − 5n

Ex. 5.20 | Q 4.4 | Page 8

Write the sequence with nth term: an = 9 − 5n

Ex. 5.20 | Q 5 | Page 8

The nth term of an A.P. is 6n + 2. Find the common difference.

 
Ex. 5.20 | Q 6.1 | Page 9

is the Consider the expression an = 2n − 1, AP . 

Ex. 5.20 | Q 6.1 | Page 9

is the Consider the expression an = 2n − 1, AP . 

Ex. 5.20 | Q 6.2 | Page 9

is the Consider the expression an = 3n2 + 1,AP .

Ex. 5.20 | Q 6.2 | Page 9

is the Consider the expression an = 3n2 + 1,AP .

Ex. 5.20 | Q 6.3 | Page 9

is the Consider the expression an = 1 + n + n2, AP .a

Ex. 5.20 | Q 6.3 | Page 9

is the Consider the expression an = 1 + n + n2, AP .a

Chapter 5: Arithmetic Progression Exercise 5.30 solutions [Page 11]

Ex. 5.30 | Q 1.1 | Page 11

For the following arithmetic progressions write the first term a and the common difference d:

 −5, −1, 3, 7, ...

Ex. 5.30 | Q 1.1 | Page 11

For the following arithmetic progressions write the first term a and the common difference d:

 −5, −1, 3, 7, ...

Ex. 5.30 | Q 1.2 | Page 11

For the following arithmetic progressions write the first term a and the common difference d:

`1/5, 3/5, 5/5, 7/5`

Ex. 5.30 | Q 1.2 | Page 11

For the following arithmetic progressions write the first term a and the common difference d:

`1/5, 3/5, 5/5, 7/5`

Ex. 5.30 | Q 1.3 | Page 11

For the following arithmetic progressions write the first term a and the common difference d:

0.3, 0.55, 0.80, 1.05, ...

Ex. 5.30 | Q 1.3 | Page 11

For the following arithmetic progressions write the first term a and the common difference d:

0.3, 0.55, 0.80, 1.05, ...

Ex. 5.30 | Q 1.4 | Page 11

For the following arithmetic progressions write the first term a and the common difference d:

−1.1, −3.1, −5.1, −7.1, ...

Ex. 5.30 | Q 1.4 | Page 11

For the following arithmetic progressions write the first term a and the common difference d:

−1.1, −3.1, −5.1, −7.1, ...

Ex. 5.30 | Q 2.1 | Page 11

Write the arithmetic progressions write the first term a and common difference d is as follows:

a = 4,d = -3

Ex. 5.30 | Q 2.1 | Page 11

Write the arithmetic progressions write the first term a and common difference d is as follows:

a = 4,d = -3

Ex. 5.30 | Q 2.2 | Page 11

Write the arithmetic progressions write the first term a and common difference d is as follows:

`a = -1, d = 1/2`

 

Ex. 5.30 | Q 2.2 | Page 11

Write the arithmetic progressions write the first term a and common difference d is as follows:

`a = -1, d = 1/2`

 

Ex. 5.30 | Q 2.3 | Page 11

Write the arithmetic progressions write the first term a and common difference d is as follows:

a = -1.5, d = -0.5

Ex. 5.30 | Q 2.3 | Page 11

Write the arithmetic progressions write the first term a and common difference d is as follows:

a = -1.5, d = -0.5

Ex. 5.30 | Q 3.1 | Page 11

In the following situations, the sequence of numbers formed will form an A.P.?

The cost of digging a well for the first metre is Rs 150 and rises by Rs 20 for each succeeding metre.

Ex. 5.30 | Q 3.1 | Page 11

In the following situations, the sequence of numbers formed will form an A.P.?

The cost of digging a well for the first metre is Rs 150 and rises by Rs 20 for each succeeding metre.

Ex. 5.30 | Q 3.2 | Page 11

In which of the following situations, does the list of numbers involved make an arithmetic progression and why?

The amount of air present in a cylinder when a vacuum pump removes 1/4 of the air remaining in the cylinder at a time.

Ex. 5.30 | Q 3.2 | Page 11

In which of the following situations, does the list of numbers involved make an arithmetic progression and why?

The amount of air present in a cylinder when a vacuum pump removes 1/4 of the air remaining in the cylinder at a time.

Ex. 5.30 | Q 4.1 | Page 11

Find the common difference and write the next four terms of each of the following arithmetic progressions:

1, −2, −5, −8, ...

Ex. 5.30 | Q 4.1 | Page 11

Find the common difference and write the next four terms of each of the following arithmetic progressions:

1, −2, −5, −8, ...

Ex. 5.30 | Q 4.2 | Page 11

Find the common difference and write the next four terms of each of the following arithmetic progressions:

0, −3, −6, −9, ...

Ex. 5.30 | Q 4.2 | Page 11

Find the common difference and write the next four terms of each of the following arithmetic progressions:

0, −3, −6, −9, ...

Ex. 5.30 | Q 4.3 | Page 11

Find the common difference and write the next four terms of each of the following arithmetic progressions:

`-1, 1/4, 3/2 .....`

Ex. 5.30 | Q 4.3 | Page 11

Find the common difference and write the next four terms of each of the following arithmetic progressions:

`-1, 1/4, 3/2 .....`

Ex. 5.30 | Q 4.4 | Page 11

Find the common difference and write the next four terms of the following arithmetic progressions:

`-1, (-5)/6, (-2)/3`

Ex. 5.30 | Q 4.4 | Page 11

Find the common difference and write the next four terms of the following arithmetic progressions:

`-1, (-5)/6, (-2)/3`

Ex. 5.30 | Q 5 | Page 11

Prove that no matter what the real numbers a and are, the sequence with the nth term a + nb is always an A.P. What is the common difference?

Ex. 5.30 | Q 5 | Page 11

Prove that no matter what the real numbers a and are, the sequence with the nth term a + nb is always an A.P. What is the common difference?

Ex. 5.30 | Q 6.01 | Page 11

Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.

3, 6, 12, 24, ...

Ex. 5.30 | Q 6.01 | Page 11

Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.

3, 6, 12, 24, ...

Ex. 5.30 | Q 6.02 | Page 11

Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.

0, −4, −8, −12, ...

Ex. 5.30 | Q 6.02 | Page 11

Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.

0, −4, −8, −12, ...

Ex. 5.30 | Q 6.03 | Page 11

Which of the following sequences are arithmetic progressions . For those which are arithmetic progressions, find out the common difference.

`1/2, 1/4, 1/6, 1/8 ......`

Ex. 5.30 | Q 6.03 | Page 11

Which of the following sequences are arithmetic progressions . For those which are arithmetic progressions, find out the common difference.

`1/2, 1/4, 1/6, 1/8 ......`

Ex. 5.30 | Q 6.04 | Page 11

Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.

12, 2, −8, −18, ...

Ex. 5.30 | Q 6.04 | Page 11

Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.

12, 2, −8, −18, ...

Ex. 5.30 | Q 6.05 | Page 11

Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.

3, 3, 3, 3, .....

Ex. 5.30 | Q 6.05 | Page 11

Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.

3, 3, 3, 3, .....

Ex. 5.30 | Q 6.06 | Page 11

Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.

p, p + 90, p + 180 p + 270, ... where p = (999)999

Ex. 5.30 | Q 6.06 | Page 11

Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.

p, p + 90, p + 180 p + 270, ... where p = (999)999

Ex. 5.30 | Q 6.07 | Page 11

Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.

1.0, 1.7, 2.4, 3.1, ...

Ex. 5.30 | Q 6.07 | Page 11

Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.

1.0, 1.7, 2.4, 3.1, ...

Ex. 5.30 | Q 6.08 | Page 11

Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.

−225, −425, −625, −825, ...

Ex. 5.30 | Q 6.08 | Page 11

Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.

−225, −425, −625, −825, ...

Ex. 5.30 | Q 6.09 | Page 11

Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.

10, 10 + 25, 10 + 26, 10 + 27,...

Ex. 5.30 | Q 6.09 | Page 11

Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.

10, 10 + 25, 10 + 26, 10 + 27,...

Ex. 5.30 | Q 6.1 | Page 11

Which of the following sequences is arithmetic progressions. For is arithmetic progression, find out the common difference.

a + b, (a + 1) + b, (a + 1) + (b + 1), (a + 2) + (b + 1), (a + 2) + (b + 2), ...

Ex. 5.30 | Q 6.1 | Page 11

Which of the following sequences is arithmetic progressions. For is arithmetic progression, find out the common difference.

a + b, (a + 1) + b, (a + 1) + (b + 1), (a + 2) + (b + 1), (a + 2) + (b + 2), ...

Ex. 5.30 | Q 6.11 | Page 11

Which of the following sequences is arithmetic progressions. For is arithmetic progression, find out the common difference.

12, 32, 52, 72, ...

Ex. 5.30 | Q 6.11 | Page 11

Which of the following sequences is arithmetic progressions. For is arithmetic progression, find out the common difference.

12, 32, 52, 72, ...

Ex. 5.30 | Q 6.12 | Page 11

Which of the following sequences is arithmetic progressions. For is arithmetic progression, find out the common difference.

12, 52, 72, 73, ...

Ex. 5.30 | Q 6.12 | Page 11

Which of the following sequences is arithmetic progressions. For is arithmetic progression, find out the common difference.

12, 52, 72, 73, ...

Ex. 5.30 | Q 7.1 | Page 11

Find the common difference of the A.P. and write the next two terms  51, 59, 67, 75, ..

Ex. 5.30 | Q 7.1 | Page 11

Find the common difference of the A.P. and write the next two terms  51, 59, 67, 75, ..

Ex. 5.30 | Q 7.2 | Page 11

Find the common difference of the A.P. and write the next two terms 75, 67, 59, 51, ...

Ex. 5.30 | Q 7.2 | Page 11

Find the common difference of the A.P. and write the next two terms 75, 67, 59, 51, ...

Ex. 5.30 | Q 7.3 | Page 11

Find the common difference of the A.P. and write the next two terms  1.8, 2.0, 2.2, 2.4, ...

Ex. 5.30 | Q 7.3 | Page 11

Find the common difference of the A.P. and write the next two terms  1.8, 2.0, 2.2, 2.4, ...

Ex. 5.30 | Q 7.4 | Page 11

Find the common difference of the A.P. and write the next two terms  \[0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, . . . \]

Ex. 5.30 | Q 7.4 | Page 11

Find the common difference of the A.P. and write the next two terms  \[0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, . . . \]

Ex. 5.30 | Q 7.5 | Page 11

Find the common difference of the A.P. and write the next two terms  119, 136, 153, 170, ... 

Ex. 5.30 | Q 7.5 | Page 11

Find the common difference of the A.P. and write the next two terms  119, 136, 153, 170, ... 

Chapter 5: Arithmetic Progression Exercise 5.40 solutions [Pages 24 - 26]

Ex. 5.40 | Q 1.1 | Page 24

Find the 10th term of the AP 1,4, 7, 10….

Ex. 5.40 | Q 1.1 | Page 24

Find the 10th term of the AP 1,4, 7, 10….

Ex. 5.40 | Q 1.2 | Page 24

Find the 18th term of the AP `sqrt2, 3sqrt2, 5sqrt2.....`

Ex. 5.40 | Q 1.2 | Page 24

Find the 18th term of the AP `sqrt2, 3sqrt2, 5sqrt2.....`

Ex. 5.40 | Q 1.3 | Page 24

Find the nth term of the A.P. 13, 8, 3, −2, ...

Ex. 5.40 | Q 1.3 | Page 24

Find the nth term of the A.P. 13, 8, 3, −2, ...

Ex. 5.40 | Q 1.4 | Page 24

Find the 10th term of the A.P. −40, −15, 10, 35, ...

Ex. 5.40 | Q 1.4 | Page 24

Find the 10th term of the A.P. −40, −15, 10, 35, ...

Ex. 5.40 | Q 1.5 | Page 24

Find 8th term of the A.P. 117, 104, 91, 78, ...

Ex. 5.40 | Q 1.5 | Page 24

Find 8th term of the A.P. 117, 104, 91, 78, ...

Ex. 5.40 | Q 1.6 | Page 24

Find 11th term of the A.P. 10.0, 10.5, 11.0, 11.5, ...

Ex. 5.40 | Q 1.6 | Page 24

Find 11th term of the A.P. 10.0, 10.5, 11.0, 11.5, ...

Ex. 5.40 | Q 1.7 | Page 24

Find 9th term of the A.P `3/4, 5/4, 7/4, 9/4,.....`

Ex. 5.40 | Q 1.7 | Page 24

Find 9th term of the A.P `3/4, 5/4, 7/4, 9/4,.....`

Ex. 5.40 | Q 2.1 | Page 24

Which term of the A.P. 3, 8, 13, ... is 248?

Ex. 5.40 | Q 2.2 | Page 24

Which term of the A.P. 84, 80, 76, ... is 248?

Ex. 5.40 | Q 2.3 | Page 24

Which term of the A.P. 4, 9, 14, ... is 254?

Ex. 5.40 | Q 2.4 | Page 24

Which term of the A.P. 21, 42, 63, 84, ... is 420?

Ex. 5.40 | Q 2.5 | Page 24

Which term of the A.P. 121, 117, 113 … is its first negative term? [Hint: Find n for an < 0]

Ex. 5.40 | Q 2.5 | Page 24

Which term of the A.P. 121, 117, 113 … is its first negative term? [Hint: Find n for an < 0]

Ex. 5.40 | Q 3.1 | Page 24

Find Is 68 a term of the A.P. 7, 10, 13, ...?

Ex. 5.40 | Q 3.1 | Page 24

Find Is 68 a term of the A.P. 7, 10, 13, ...?

Ex. 5.40 | Q 3.2 | Page 24

Is 302 a term of the A.P. 3, 8, 13, ...?

Ex. 5.40 | Q 3.2 | Page 24

Is 302 a term of the A.P. 3, 8, 13, ...?

Ex. 5.40 | Q 3.3 | Page 24

Is -150 a term of the A.P. 11, 8, 5, 2, ...?

Ex. 5.40 | Q 3.3 | Page 24

Is -150 a term of the A.P. 11, 8, 5, 2, ...?

Ex. 5.40 | Q 4.1 | Page 24

How many terms are there in the A.P.?

7, 10, 13, ... 43.

Ex. 5.40 | Q 4.1 | Page 24

How many terms are there in the A.P.?

7, 10, 13, ... 43.

Ex. 5.40 | Q 4.2 | Page 24

How many terms are there in the A.P.?

`-1, 5/6, 2/3, 1/2,.....10/3`

Ex. 5.40 | Q 4.2 | Page 24

How many terms are there in the A.P.?

`-1, 5/6, 2/3, 1/2,.....10/3`

Ex. 5.40 | Q 4.3 | Page 24

Find the number of terms in the following A.P. : 7, 13, 19, . . . , 205

Ex. 5.40 | Q 4.4 | Page 24

How many terms are there in the AP?

`18, 15 1/2, 13, ............ -47`

Ex. 5.40 | Q 4.4 | Page 24

How many terms are there in the AP?

`18, 15 1/2, 13, ............ -47`

Ex. 5.40 | Q 5 | Page 24

The first term of an A.P. is 5, the common difference is 3 and the last term is 80;

Ex. 5.40 | Q 5 | Page 24

The first term of an A.P. is 5, the common difference is 3 and the last term is 80;

Ex. 5.40 | Q 6 | Page 24

The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.

Ex. 5.40 | Q 6 | Page 24

The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.

Ex. 5.40 | Q 7 | Page 24

If the 9th term of an A.P. is zero, then prove that 29th term is double of 19th term.

Ex. 5.40 | Q 7 | Page 24

If the 9th term of an A.P. is zero, then prove that 29th term is double of 19th term.

Ex. 5.40 | Q 8 | Page 24

If 10 times the 10th term of an A.P. is equal to 15 times the 15th term, show that 25th term of the A.P. is zero.

Ex. 5.40 | Q 8 | Page 24

If 10 times the 10th term of an A.P. is equal to 15 times the 15th term, show that 25th term of the A.P. is zero.

Ex. 5.40 | Q 9 | Page 24

The 10th and 18th terms of an A.P. are 41 and 73 respectively. Find 26th term.

Ex. 5.40 | Q 9 | Page 24

The 10th and 18th terms of an A.P. are 41 and 73 respectively. Find 26th term.

Ex. 5.40 | Q 10 | Page 24

In a certain A.P. the 24th term is twice the 10th term. Prove that the 72nd term is twice the 34th term.

Ex. 5.40 | Q 12 | Page 25

If the nth term of the A.P. 9, 7, 5, ... is same as the nth term of the A.P. 15, 12, 9, ... find n.

Ex. 5.40 | Q 12 | Page 25

If the nth term of the A.P. 9, 7, 5, ... is same as the nth term of the A.P. 15, 12, 9, ... find n.

Ex. 5.40 | Q 13.1 | Page 25

Find the 12th term from the end of the following arithmetic progressions:

3, 5, 7, 9, ... 201

Ex. 5.40 | Q 13.1 | Page 25

Find the 12th term from the end of the following arithmetic progressions:

3, 5, 7, 9, ... 201

Ex. 5.40 | Q 13.2 | Page 25

Find the 12th term from the end of the following arithmetic progressions:

3, 8, 13, ..., 253

Ex. 5.40 | Q 13.3 | Page 25

Find the 12th term from the end of the following arithmetic progressions:

1, 4, 7, 10, ..., 88

Ex. 5.40 | Q 14 | Page 25

The 4th term of an A.P. is three times the first and the 7th term exceeds twice the third term by 1. Find the first term and the common difference.

Ex. 5.40 | Q 15 | Page 25

Find the second term and nth term of an A.P. whose 6th term is 12 and 8th term is 22.

Ex. 5.40 | Q 16 | Page 25

How many numbers of two digit are divisible by 3?

Ex. 5.40 | Q 17 | Page 25

An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find the 32nd term.

Ex. 5.40 | Q 18 | Page 25

The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 34. Find the first term and the common difference of the A.P.

Ex. 5.40 | Q 19 | Page 25

The first term of an A.P. is 5 and its 100th term is -292. Find the 50th term of this A.P.

Ex. 5.40 | Q 20.1 | Page 25

Find a30 − a20 for the A.P.

−9, −14, −19, −24, ...

Ex. 5.40 | Q 20.1 | Page 25

Find a30 − a20 for the A.P.

−9, −14, −19, −24, ...

Ex. 5.40 | Q 20.2 | Page 25

Find a30 − a20 for the A.P.

a,a + d, a + 2d, a + 3d, ...

Ex. 5.40 | Q 20.2 | Page 25

Find a30 − a20 for the A.P.

a,a + d, a + 2d, a + 3d, ...

Ex. 5.40 | Q 21.1 | Page 25

Write the expression an- ak for the A.P. a, a + d, a + 2d, ... Hence, find the common difference of the A.P. for which

11th term is 5 and the 13th term is 79.

Ex. 5.40 | Q 21.1 | Page 25

Write the expression an- ak for the A.P. a, a + d, a + 2d, ... Hence, find the common difference of the A.P. for which

11th term is 5 and the 13th term is 79.

Ex. 5.40 | Q 21.2 | Page 25

Write the expression an- ak for the A.P. a, a + d, a + 2d, ... Hence, find the common difference of the A.P. for which  a10 −a5 = 200

Ex. 5.40 | Q 21.2 | Page 25

Write the expression an- ak for the A.P. a, a + d, a + 2d, ... Hence, find the common difference of the A.P. for which  a10 −a5 = 200

Ex. 5.40 | Q 21.3 | Page 25

Write the expression an- ak for the A.P. a, a + d, a + 2d, ... Hence, find the common difference of the A.P. for which

20th term is 10 more than the 18th term.

Ex. 5.40 | Q 21.3 | Page 25

Write the expression an- ak for the A.P. a, a + d, a + 2d, ... Hence, find the common difference of the A.P. for which

20th term is 10 more than the 18th term.

Ex. 5.40 | Q 22.1 | Page 25

Find n if the given value of x is the nth term of the given A.P.

25, 50, 75, 100, ...; x = 1000

Ex. 5.40 | Q 22.1 | Page 25

Find n if the given value of x is the nth term of the given A.P.

25, 50, 75, 100, ...; x = 1000

Ex. 5.40 | Q 22.2 | Page 25

Find n if the given value of x is the nth term of the given A.P.

−1, −3, −5, −7, ...; x = −151

Ex. 5.40 | Q 22.2 | Page 25

Find n if the given value of x is the nth term of the given A.P.

−1, −3, −5, −7, ...; x = −151

Ex. 5.40 | Q 22.3 | Page 25

Find n if the given value of x is the nth term of the given A.P.

`5 1/2, 11, 16 1/2, 22, ......; x = 550`

Ex. 5.40 | Q 22.3 | Page 25

Find n if the given value of x is the nth term of the given A.P.

`5 1/2, 11, 16 1/2, 22, ......; x = 550`

Ex. 5.40 | Q 22.4 | Page 25

Find n if the given value of x is the nth term of the given A.P.

`1, 21/11, 31/11, 41/11,......, x = 171/11`

Ex. 5.40 | Q 22.4 | Page 25

Find n if the given value of x is the nth term of the given A.P.

`1, 21/11, 31/11, 41/11,......, x = 171/11`

Ex. 5.40 | Q 24 | Page 25

Find the arithmetic progression whose third term is 16 and the seventh term exceeds its fifth term by 12.

Ex. 5.40 | Q 24 | Page 25

Find the arithmetic progression whose third term is 16 and the seventh term exceeds its fifth term by 12.

Ex. 5.40 | Q 25 | Page 25

The 7th term of an A.P. is 32 and its 13th term is 62.  Find the A.P.

Ex. 5.40 | Q 25 | Page 25

The 7th term of an A.P. is 32 and its 13th term is 62.  Find the A.P.

Ex. 5.40 | Q 26 | Page 25

Which term of the A.P. 3, 10, 17, ... will be 84 more than its 13th term?

Ex. 5.40 | Q 26 | Page 25

Which term of the A.P. 3, 10, 17, ... will be 84 more than its 13th term?

Ex. 5.40 | Q 27 | Page 25

Two arithmetic progressions have the same common difference. The difference between their 100th terms is 100, what is the difference between their l000th terms?

Ex. 5.40 | Q 27 | Page 25

Two arithmetic progressions have the same common difference. The difference between their 100th terms is 100, what is the difference between their l000th terms?

Ex. 5.40 | Q 28 | Page 25

For what value of n, the nth terms of the arithmetic progressions 63, 65, 67, ... and 3, 10, 17, ... are equal?

Ex. 5.40 | Q 29 | Page 25

How many multiples of 4 lie between 10 and 250?

Ex. 5.40 | Q 30 | Page 25

How many three digit numbers are divisible by 7?

 
Ex. 5.40 | Q 30 | Page 25

How many three digit numbers are divisible by 7?

 
Ex. 5.40 | Q 31 | Page 25

Which term of the A.P. 8, 14, 20, 26, ... will be 72 more than its 41st term?

Ex. 5.40 | Q 32 | Page 26

Find the term of the arithmetic progression 9, 12, 15, 18, ... which is 39 more than its 36th term.

Ex. 5.40 | Q 32 | Page 26

Find the term of the arithmetic progression 9, 12, 15, 18, ... which is 39 more than its 36th term.

Ex. 5.40 | Q 33 | Page 26

Find the 8th term from the end of the A.P. 7, 10, 13, ..., 184

Ex. 5.40 | Q 33 | Page 26

Find the 8th term from the end of the A.P. 7, 10, 13, ..., 184

Ex. 5.40 | Q 34 | Page 26

Find the 10th term from the end of the A.P. 8, 10, 12, ..., 126.

Ex. 5.40 | Q 35 | Page 26

The sum of 4th and 8th terms of an A.P. is 24 and the sum of 6th and 10th terms is 44. Find the A.P.

Ex. 5.40 | Q 36 | Page 26

Which term of the A.P. 3, 15, 27, 39, ... will be 120 more than its 21st term?

Ex. 5.40 | Q 37 | Page 26

The 17th term of an A.P. is 5 more than twice its 8th term. If the 11th term of the A.P. is 43, find the nth term.

Ex. 5.40 | Q 38 | Page 26

Find the number of all three digit natural numbers which are divisible by 9.

 
Ex. 5.40 | Q 38 | Page 26

Find the number of all three digit natural numbers which are divisible by 9.

 
Ex. 5.40 | Q 39 | Page 26

The 19th term of an A.P. is equal to three times its sixth term. If its 9th term is 19, find the A.P.

Ex. 5.40 | Q 39 | Page 26

The 19th term of an A.P. is equal to three times its sixth term. If its 9th term is 19, find the A.P.

Ex. 5.40 | Q 40 | Page 26

The 9th term of an A.P. is equal to 6 times its second term. If its 5th term is 22, find the A.P.

Ex. 5.40 | Q 40 | Page 26

The 9th term of an A.P. is equal to 6 times its second term. If its 5th term is 22, find the A.P.

Ex. 5.40 | Q 41 | Page 26

The 24th term of an A.P. is twice its 10th term. Show that its 72nd term is 4 times its 15thterm.

Ex. 5.40 | Q 41 | Page 26

The 24th term of an A.P. is twice its 10th term. Show that its 72nd term is 4 times its 15thterm.

Ex. 5.40 | Q 42 | Page 26

Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.

Ex. 5.40 | Q 42 | Page 26

Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.

Ex. 5.40 | Q 43 | Page 26

If the seventh term of an A.P. is  \[\frac{1}{9}\] and its ninth term is \[\frac{1}{7}\] , find its (63)rd term.

 
  
Ex. 5.40 | Q 43 | Page 26

If the seventh term of an A.P. is  \[\frac{1}{9}\] and its ninth term is \[\frac{1}{7}\] , find its (63)rd term.

 
  
Ex. 5.40 | Q 44 | Page 26

The sum of 5th and 9th terms of an A.P. is 30. If its 25th term is three times its 8th term, find the A.P.

Ex. 5.40 | Q 44 | Page 26

The sum of 5th and 9th terms of an A.P. is 30. If its 25th term is three times its 8th term, find the A.P.

Ex. 5.40 | Q 45 | Page 26

Find where 0 (zero) is a term of the A.P. 40, 37, 34, 31, ..... .

 
Ex. 5.40 | Q 45 | Page 26

Find where 0 (zero) is a term of the A.P. 40, 37, 34, 31, ..... .

 
Ex. 5.40 | Q 46 | Page 26

Find the middle term of the A.P. 213, 205, 197, ...., 37.

 
Ex. 5.40 | Q 46 | Page 26

Find the middle term of the A.P. 213, 205, 197, ...., 37.

 
Ex. 5.40 | Q 47 | Page 26

If the 5th term of an A.P. is 31 and 25th term is 140 more than the 5th term, find the A.P.

 
Ex. 5.40 | Q 47 | Page 26

If the 5th term of an A.P. is 31 and 25th term is 140 more than the 5th term, find the A.P.

 
Ex. 5.40 | Q 49 | Page 26

If (m + 1)th term of an A.P is twice the (n + 1)th term, prove that (3m + 1)th term is twice the (m + n + 1)th term.

Ex. 5.40 | Q 49 | Page 26

If (m + 1)th term of an A.P is twice the (n + 1)th term, prove that (3m + 1)th term is twice the (m + n + 1)th term.

Ex. 5.40 | Q 50 | Page 26

If an A.P. consists of n terms with first term a and nth term show that the sum of the mth term from the beginning and the mth term from the end is (a + l).

Ex. 5.40 | Q 50 | Page 26

If an A.P. consists of n terms with first term a and nth term show that the sum of the mth term from the beginning and the mth term from the end is (a + l).

Chapter 5: Arithmetic Progression Exercise 5.50 solutions [Page 30]

Ex. 5.50 | Q 1 | Page 30

Find the value of x for which (8x + 4), (6x − 2) and (2x + 7) are in A.P.

Ex. 5.50 | Q 1 | Page 30

Find the value of x for which (8x + 4), (6x − 2) and (2x + 7) are in A.P.

Ex. 5.50 | Q 2 | Page 30

If x + 1, 3x and 4x + 2 are in A.P., find the value of x.

Ex. 5.50 | Q 2 | Page 30

If x + 1, 3x and 4x + 2 are in A.P., find the value of x.

Ex. 5.50 | Q 3 | Page 30

Show that (a − b)2, (a2 + b2) and (a + b)2 are in A.P.

Ex. 5.50 | Q 3 | Page 30

Show that (a − b)2, (a2 + b2) and (a + b)2 are in A.P.

Ex. 5.50 | Q 4 | Page 30

The sum of three terms of an A.P. is 21 and the product of the first and the third terms exceed the second term by 6, find three terms.

Ex. 5.50 | Q 4 | Page 30

The sum of three terms of an A.P. is 21 and the product of the first and the third terms exceed the second term by 6, find three terms.

Ex. 5.50 | Q 5 | Page 30

Three numbers are in A.P. If the sum of these numbers is 27 and the product 648, find the numbers.

Ex. 5.50 | Q 5 | Page 30

Three numbers are in A.P. If the sum of these numbers is 27 and the product 648, find the numbers.

Ex. 5.50 | Q 6 | Page 30

Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.

Ex. 5.50 | Q 6 | Page 30

Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.

Ex. 5.50 | Q 7 | Page 30

The sum of three numbers in A.P. is 12 and sum of their cubes is 288. Find the numbers.

Ex. 5.50 | Q 7 | Page 30

The sum of three numbers in A.P. is 12 and sum of their cubes is 288. Find the numbers.

Ex. 5.50 | Q 8 | Page 30

Let the four terms of the AP be a − 3da − da + and a + 3d. find A.P.

Ex. 5.50 | Q 8 | Page 30

Let the four terms of the AP be a − 3da − da + and a + 3d. find A.P.

Ex. 5.50 | Q 9 | Page 30

The angles of a quadrilateral are in A.P. whose common difference is 10°. Find the angles.

Ex. 5.50 | Q 9 | Page 30

The angles of a quadrilateral are in A.P. whose common difference is 10°. Find the angles.

Ex. 5.50 | Q 10 | Page 30

Suppose three parts of 207 are (a − d), a , (a + d) such that , (a + d)  >a >  (a − d). 

Ex. 5.50 | Q 10 | Page 30

Suppose three parts of 207 are (a − d), a , (a + d) such that , (a + d)  >a >  (a − d). 

Ex. 5.50 | Q 11 | Page 30

Suppose the angles of a triangle are (a − d), a , (a + d) such that , (a + d)  >a >  (a − d).

Ex. 5.50 | Q 11 | Page 30

Suppose the angles of a triangle are (a − d), a , (a + d) such that , (a + d)  >a >  (a − d).

Chapter 5: Arithmetic Progression Exercise 5.60 solutions [Pages 30 - 55]

Ex. 5.60 | Q 1.1 | Page 30

Find the sum of the following arithmetic progressions: 50, 46, 42, ... to 10 terms

Ex. 5.60 | Q 1.1 | Page 30

Find the sum of the following arithmetic progressions: 50, 46, 42, ... to 10 terms

Ex. 5.60 | Q 1.2 | Page 30

Find the sum of the following arithmetic progressions:

1, 3, 5, 7, ... to 12 terms

Ex. 5.60 | Q 1.2 | Page 30

Find the sum of the following arithmetic progressions:

1, 3, 5, 7, ... to 12 terms

Ex. 5.60 | Q 1.3 | Page 30

Find the sum of the following arithmetic progressions:

3, 9/2, 6, 15/2, ... to 25 terms

Ex. 5.60 | Q 1.3 | Page 30

Find the sum of the following arithmetic progressions:

3, 9/2, 6, 15/2, ... to 25 terms

Ex. 5.60 | Q 1.4 | Page 30

Find the sum of the following arithmetic progressions:

41, 36, 31, ... to 12 terms

Ex. 5.60 | Q 1.4 | Page 30

Find the sum of the following arithmetic progressions:

41, 36, 31, ... to 12 terms

Ex. 5.60 | Q 1.5 | Page 30

Find the sum of the following arithmetic progressions:

a + b, a − b, a − 3b, ... to 22 terms

Ex. 5.60 | Q 1.5 | Page 30

Find the sum of the following arithmetic progressions:

a + b, a − b, a − 3b, ... to 22 terms

Ex. 5.60 | Q 1.6 | Page 30

Find the sum of the following arithmetic progressions 

`(x - y)^2,(x^2 + y^2), (x + y)^2,.... to n term`

Ex. 5.60 | Q 1.6 | Page 30

Find the sum of the following arithmetic progressions 

`(x - y)^2,(x^2 + y^2), (x + y)^2,.... to n term`

Ex. 5.60 | Q 1.7 | Page 30

Find the sum of the following arithmetic progressions:

`(x - y)/(x + y),(3x - 2y)/(x + y), (5x - 3y)/(x + y)`,  .....to n terms

Ex. 5.60 | Q 1.7 | Page 30

Find the sum of the following arithmetic progressions:

`(x - y)/(x + y),(3x - 2y)/(x + y), (5x - 3y)/(x + y)`,  .....to n terms

Ex. 5.60 | Q 1.8 | Page 30

Find the sum of the following arithmetic progressions:

−26, −24, −22, …. to 36 terms

Ex. 5.60 | Q 1.8 | Page 30

Find the sum of the following arithmetic progressions:

−26, −24, −22, …. to 36 terms

Ex. 5.60 | Q 2 | Page 51

Find the sum to n term of the A.P. 5, 2, −1, −4, −7, ...,

Ex. 5.60 | Q 2 | Page 51

Find the sum to n term of the A.P. 5, 2, −1, −4, −7, ...,

Ex. 5.60 | Q 3 | Page 51

Find the sum of n terms of an A.P. whose nth terms is given by an = 5 − 6n.

Ex. 5.60 | Q 3 | Page 51

Find the sum of n terms of an A.P. whose nth terms is given by an = 5 − 6n.

Ex. 5.60 | Q 4 | Page 51

The term  A.P is 8, 10, 12, 14,...., 126 . find A.P.

Ex. 5.60 | Q 4 | Page 51

The term  A.P is 8, 10, 12, 14,...., 126 . find A.P.

Ex. 5.60 | Q 5.1 | Page 51

Find the sum of the first 15 terms of each of the following sequences having the nth term as

`a_n = 3 + 4n`

Ex. 5.60 | Q 5.1 | Page 51

Find the sum of the first 15 terms of each of the following sequences having the nth term as

`a_n = 3 + 4n`

Ex. 5.60 | Q 5.2 | Page 51

Find the sum of the first 15 terms of each of the following sequences having the nth term as

bn = 5 + 2n

Ex. 5.60 | Q 5.2 | Page 51

Find the sum of the first 15 terms of each of the following sequences having the nth term as

bn = 5 + 2n

Ex. 5.60 | Q 5.3 | Page 51

Find the sum of the first 15 terms of each of the following sequences having nth term as  xn = 6 − n .

Ex. 5.60 | Q 5.3 | Page 51

Find the sum of the first 15 terms of each of the following sequences having nth term as  xn = 6 − n .

Ex. 5.60 | Q 5.4 | Page 51

Find the sum of the first 15 terms of each of the following sequences having the nth term as

yn = 9 − 5n

Ex. 5.60 | Q 5.4 | Page 51

Find the sum of the first 15 terms of each of the following sequences having the nth term as

yn = 9 − 5n

Ex. 5.60 | Q 6 | Page 51

Find the sum of first 20 terms of the sequence whose nth term is `a_n = An + B`

Ex. 5.60 | Q 6 | Page 51

Find the sum of first 20 terms of the sequence whose nth term is `a_n = An + B`

Ex. 5.60 | Q 7 | Page 51

Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 2 − 3n.

Ex. 5.60 | Q 7 | Page 51

Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 2 − 3n.

Ex. 5.60 | Q 8 | Page 51

Find the sum of the first 25 terms of an A.P. whose nth term is given by a= 7 − 3n

Ex. 5.60 | Q 8 | Page 51

Find the sum of the first 25 terms of an A.P. whose nth term is given by a= 7 − 3n

Ex. 5.60 | Q 9 | Page 51

If the sum of a certain number of terms starting from first term of an A.P. is 25, 22, 19, ..., is 116. Find the last term.

Ex. 5.60 | Q 9 | Page 51

If the sum of a certain number of terms starting from first term of an A.P. is 25, 22, 19, ..., is 116. Find the last term.

Ex. 5.60 | Q 10.1 | Page 51

How many terms of the A.P. 18, 16, 14, .... be taken so that their sum is zero?

Ex. 5.60 | Q 10.1 | Page 51

How many terms of the A.P. 18, 16, 14, .... be taken so that their sum is zero?

Ex. 5.60 | Q 10.2 | Page 51

How many terms are there in the A.P. whose first and fifth terms are −14 and 2 respectively and the sum of the terms is 40?

Ex. 5.60 | Q 10.2 | Page 51

How many terms are there in the A.P. whose first and fifth terms are −14 and 2 respectively and the sum of the terms is 40?

Ex. 5.60 | Q 10.3 | Page 51

How many terms of the A.P. 9, 17, 25, . . . must be taken so that their sum is 636?

Ex. 5.60 | Q 10.3 | Page 51

How many terms of the A.P. 9, 17, 25, . . . must be taken so that their sum is 636?

Ex. 5.60 | Q 10.4 | Page 51

How many terms of the A.P. 63, 60, 57, ... must be taken so that their sum is 693?

Ex. 5.60 | Q 10.4 | Page 51

How many terms of the A.P. 63, 60, 57, ... must be taken so that their sum is 693?

Ex. 5.60 | Q 11.1 | Page 51

Find the sum of the first 11 terms of the A.P : 2, 6, 10, 14, ...

Ex. 5.60 | Q 11.1 | Page 51

Find the sum of the first 11 terms of the A.P : 2, 6, 10, 14, ...

Ex. 5.60 | Q 11.2 | Page 51

Find the sum of the first 13 terms of the A.P: -6, 0, 6, 12,....

Ex. 5.60 | Q 11.2 | Page 51

Find the sum of the first 13 terms of the A.P: -6, 0, 6, 12,....

Ex. 5.60 | Q 11.3 | Page 51

Find the sum of the first 51 terms of the A.P: whose second term is 2 and the fourth term is 8.

Ex. 5.60 | Q 11.3 | Page 51

Find the sum of the first 51 terms of the A.P: whose second term is 2 and the fourth term is 8.

Ex. 5.60 | Q 12.1 | Page 51

Find the sum of first 15 multiples of 8.

Ex. 5.60 | Q 12.1 | Page 51

Find the sum of first 15 multiples of 8.

Ex. 5.60 | Q 12.2 | Page 51

Find the sum of first 40 positive integers divisible by 6.

Ex. 5.60 | Q 12.2 | Page 51

Find the sum of the first 40 positive integers divisible by 3

Ex. 5.60 | Q 12.2 | Page 51

Find the sum of the first 40 positive integers divisible by 3

Ex. 5.60 | Q 12.2 | Page 51

Find the sum of the first 40 positive integers divisible by 5

Ex. 5.60 | Q 12.2 | Page 51

Find the sum of first 40 positive integers divisible by 6.

Ex. 5.60 | Q 12.2 | Page 51

Find the sum of the first 40 positive integers divisible by 5

Ex. 5.60 | Q 12.3 | Page 51

Find the sum of all 3 - digit natural numbers which are divisible by 13.

Ex. 5.60 | Q 12.3 | Page 51

Find the sum of all 3 - digit natural numbers which are divisible by 13.

Ex. 5.60 | Q 12.4 | Page 51

Find the sum of all 3-digit natural numbers, which are multiples of 11.

Ex. 5.60 | Q 12.4 | Page 51

Find the sum of all 3-digit natural numbers, which are multiples of 11.

Ex. 5.60 | Q 12.5 | Page 51

Find the sum of  all 2 - digit natural numbers divisible by 4.

Ex. 5.60 | Q 12.5 | Page 51

Find the sum of  all 2 - digit natural numbers divisible by 4.

Ex. 5.60 | Q 13.1 | Page 51

Find the sum 2 + 4 + 6 ... + 200

Ex. 5.60 | Q 13.1 | Page 51

Find the sum 2 + 4 + 6 ... + 200

Ex. 5.60 | Q 13.2 | Page 51

Find the sum 3 + 11 + 19 + ... + 803

Ex. 5.60 | Q 13.2 | Page 51

Find the sum 3 + 11 + 19 + ... + 803

Ex. 5.60 | Q 13.3 | Page 51

Find the sum  (−5) + (−8)+ (−11) + ... + (−230) .

Ex. 5.60 | Q 13.3 | Page 51

Find the sum  (−5) + (−8)+ (−11) + ... + (−230) .

Ex. 5.60 | Q 13.4 | Page 51

Find the sum:  1 + 3 + 5 + 7 + ... + 199 .

Ex. 5.60 | Q 13.4 | Page 51

Find the sum:  1 + 3 + 5 + 7 + ... + 199 .

Ex. 5.60 | Q 13.5 | Page 51

Find the sum \[7 + 10\frac{1}{2} + 14 + . . . + 84\]

 

Ex. 5.60 | Q 13.5 | Page 51

Find the sum \[7 + 10\frac{1}{2} + 14 + . . . + 84\]

 

Ex. 5.60 | Q 13.6 | Page 51

Find the sums given below :

34 + 32 + 30 + . . . + 10

Ex. 5.60 | Q 13.6 | Page 51

Find the sums given below :

34 + 32 + 30 + . . . + 10

Ex. 5.60 | Q 13.7 | Page 51

Find the sum 25 + 28 + 31 + ….. + 100

Ex. 5.60 | Q 13.7 | Page 51

Find the sum 25 + 28 + 31 + ….. + 100

Ex. 5.60 | Q 13.8 | Page 51
Find the sum:  \[18 + 15\frac{1}{2} + 13 + . . . + \left( - 49\frac{1}{2} \right)\]

 

Ex. 5.60 | Q 13.8 | Page 51
Find the sum:  \[18 + 15\frac{1}{2} + 13 + . . . + \left( - 49\frac{1}{2} \right)\]

 

Ex. 5.60 | Q 14 | Page 52

the first and the last terms of an A.P. are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?

Ex. 5.60 | Q 14 | Page 52

the first and the last terms of an A.P. are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?

Ex. 5.60 | Q 15 | Page 52

The third term of an A.P. is 7 and the seventh term exceeds three times the third term by 2. Find the first term, the common difference and the sum of first 20 terms.

Ex. 5.60 | Q 16 | Page 52

The first term of an A.P. is 2 and the last term is 50. The sum of all these terms is 442. Find the common difference.

Ex. 5.60 | Q 17 | Page 52

If the 12th term of an A.P. is −13 and the sum of the first four terms is 24, what is the sum of first 10 terms?

Ex. 5.60 | Q 17 | Page 52

If the 12th term of an A.P. is −13 and the sum of the first four terms is 24, what is the sum of first 10 terms?

Ex. 5.60 | Q 18 | Page 52

Find the sum of n terms of the series \[\left( 4 - \frac{1}{n} \right) + \left( 4 - \frac{2}{n} \right) + \left( 4 - \frac{3}{n} \right) + . . . . . . . . . .\]

Ex. 5.60 | Q 18 | Page 52

Find the sum of n terms of the series \[\left( 4 - \frac{1}{n} \right) + \left( 4 - \frac{2}{n} \right) + \left( 4 - \frac{3}{n} \right) + . . . . . . . . . .\]

Ex. 5.60 | Q 19 | Page 52

In an A.P., if the first term is 22, the common difference is −4 and the sum to n terms is 64,  find n.

Ex. 5.60 | Q 19 | Page 52

In an A.P., if the first term is 22, the common difference is −4 and the sum to n terms is 64,  find n.

Ex. 5.60 | Q 20 | Page 52

In an A.P., if the 5th and 12th terms are 30 and 65 respectively, what is the sum of first 20 terms?

Ex. 5.60 | Q 20 | Page 52

In an A.P., if the 5th and 12th terms are 30 and 65 respectively, what is the sum of first 20 terms?

Ex. 5.60 | Q 21 | Page 52

Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.

Ex. 5.60 | Q 21 | Page 52

Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.

Ex. 5.60 | Q 22 | Page 52

If the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P.

Ex. 5.60 | Q 22 | Page 52

If the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P.

Ex. 5.60 | Q 23 | Page 52

The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

Ex. 5.60 | Q 23 | Page 52

The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

Ex. 5.60 | Q 24 | Page 52

In an A.P. the first term is 8, nth term is 33 and the sum to first n terms is 123. Find n and d, the common differences.

Ex. 5.60 | Q 24 | Page 52

In an A.P. the first term is 8, nth term is 33 and the sum to first n terms is 123. Find n and d, the common differences.

Ex. 5.60 | Q 25 | Page 52

In an A.P., the first term is 22, nth term is −11 and the sum to first n terms is 66. Find n and d, the common difference

Ex. 5.60 | Q 25 | Page 52

In an A.P., the first term is 22, nth term is −11 and the sum to first n terms is 66. Find n and d, the common difference

Ex. 5.60 | Q 26 | Page 52

​The first and the last terms of an A.P. are 7 and 49 respectively. If sum of all its terms is 420, find its common difference. 

Ex. 5.60 | Q 26 | Page 52

​The first and the last terms of an A.P. are 7 and 49 respectively. If sum of all its terms is 420, find its common difference. 

Ex. 5.60 | Q 27 | Page 52

The first and the last terms of an A.P. are 5 and 45 respectively. If the sum of all its terms is 400, find its common difference.

Ex. 5.60 | Q 27 | Page 52

The first and the last terms of an A.P. are 5 and 45 respectively. If the sum of all its terms is 400, find its common difference.

Ex. 5.60 | Q 28 | Page 52

The sum of first 9 terms of an A.P. is 162. The ratio of its 6th term to its 13th term is 1 : 2. Find the first and 15th term of the A.P.

Ex. 5.60 | Q 28 | Page 52

The sum of first 9 terms of an A.P. is 162. The ratio of its 6th term to its 13th term is 1 : 2. Find the first and 15th term of the A.P.

Ex. 5.60 | Q 29 | Page 52

If the 10th term of an A.P. is 21 and the sum of its first 10 terms is 120, find its nth term.

 
Ex. 5.60 | Q 29 | Page 52

If the 10th term of an A.P. is 21 and the sum of its first 10 terms is 120, find its nth term.

 
Ex. 5.60 | Q 30 | Page 52

The sum of the first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161. Find the 28th term of this A.P.

Ex. 5.60 | Q 30 | Page 52

The sum of the first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161. Find the 28th term of this A.P.

Ex. 5.60 | Q 31 | Page 52

The sum of first seven terms of an A.P. is 182. If its 4th and the 17th terms are in the ratio 1 : 5, find the A.P.

Ex. 5.60 | Q 31 | Page 52

The sum of first seven terms of an A.P. is 182. If its 4th and the 17th terms are in the ratio 1 : 5, find the A.P.

Ex. 5.60 | Q 32 | Page 52

The nth term of an AP is given by (−4n + 15). Find the sum of first 20 terms of this AP?

Ex. 5.60 | Q 32 | Page 52

The nth term of an AP is given by (−4n + 15). Find the sum of first 20 terms of this AP?

Ex. 5.60 | Q 33 | Page 52

In an A.P., the sum of first ten terms is −150 and the sum of its next ten terms is −550. Find the A.P.

Ex. 5.60 | Q 33 | Page 52

In an A.P., the sum of first ten terms is −150 and the sum of its next ten terms is −550. Find the A.P.

Ex. 5.60 | Q 34 | Page 52

Sum of the first 14 terms of and AP is 1505 and its first term is 10. Find its 25th term. 

Ex. 5.60 | Q 35 | Page 52

In an AP, the first term is 2, the last term is 29 and the sum of all the terms is 155. Find the common difference.

Ex. 5.60 | Q 36 | Page 53

the first and the last terms of an A.P. are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?

Ex. 5.60 | Q 36 | Page 53

the first and the last terms of an A.P. are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?

Ex. 5.60 | Q 37 | Page 53

Find the number of terms of the AP − 12, −9, −6, ….., 12. If 1 is added to each term of this AP, then find the sum of all terms of the AP thus obtained ?

Ex. 5.60 | Q 38 | Page 53

The sum of the first n terms of an A.P. is 3n2 + 6n. Find the nth term of this A.P.

 
Ex. 5.60 | Q 38 | Page 53

The sum of the first n terms of an A.P. is 3n2 + 6n. Find the nth term of this A.P.

 
Ex. 5.60 | Q 39 | Page 53

The sum of first n terms of an A.P. is 5n − n2. Find the nth term of this A.P.

 
Ex. 5.60 | Q 39 | Page 53

The sum of first n terms of an A.P. is 5n − n2. Find the nth term of this A.P.

 
Ex. 5.60 | Q 40 | Page 53

The sum of the first n terms of an A.P. is 4n2 + 2n. Find the nth term of this A.P.

 
Ex. 5.60 | Q 40 | Page 53

The sum of the first n terms of an A.P. is 4n2 + 2n. Find the nth term of this A.P.

 
Ex. 5.60 | Q 41 | Page 53

The sum of first n terms of an A.P. is 3n2 + 4n. Find the 25th term of this A.P.

 
Ex. 5.60 | Q 41 | Page 53

The sum of first n terms of an A.P. is 3n2 + 4n. Find the 25th term of this A.P.

 
Ex. 5.60 | Q 42 | Page 53

The sum of first n terms of an A.P is 5n2 + 3n. If its mth terms is 168, find the value of m. Also, find the 20th term of this A.P.

 
Ex. 5.60 | Q 42 | Page 53

The sum of first n terms of an A.P is 5n2 + 3n. If its mth terms is 168, find the value of m. Also, find the 20th term of this A.P.

 
Ex. 5.60 | Q 43 | Page 53

The sum of first q terms of an AP is  (63q - 3q2) . If its pth term is -60, find the value of p. Also, find the 11th term of its AP. 

Ex. 5.60 | Q 44 | Page 53

The sum of fist m terms of an AP is ( 4m2  - m). If its nth term is 107, find the value of n. Also, Find the 21st term of this AP. 

Ex. 5.60 | Q 45 | Page 53

If the sum of the first n terms of an AP is 4n − n2, what is the first term (that is S1)? What is the sum of first two terms? What is the second term? Similarly find the 3rd, the10th and the nth terms.

Ex. 5.60 | Q 45 | Page 53

If the sum of the first n terms of an AP is 4n − n2, what is the first term (that is S1)? What is the sum of first two terms? What is the second term? Similarly find the 3rd, the10th and the nth terms.

Ex. 5.60 | Q 46 | Page 53

If the sum of first n terms of an A.P. is  \[\frac{1}{2}\] (3n2 + 7n), then find its nth term. Hence write its 20th term.

 
 
Ex. 5.60 | Q 46 | Page 53

If the sum of first n terms of an A.P. is  \[\frac{1}{2}\] (3n2 + 7n), then find its nth term. Hence write its 20th term.

 
 
Ex. 5.60 | Q 47 | Page 53

In an A.P., the sum of first n terms is `(3n^2)/2 + 13/2 n`. Find its 25th term.

Ex. 5.60 | Q 47 | Page 53

In an A.P., the sum of first n terms is `(3n^2)/2 + 13/2 n`. Find its 25th term.

Ex. 5.60 | Q 48 | Page 53

Find the sum of all natural numbers between 1 and 100, which are divisible by 3.

Ex. 5.60 | Q 48 | Page 53

Find the sum of all natural numbers between 1 and 100, which are divisible by 3.

Ex. 5.60 | Q 49 | Page 53

Find the sum of first n odd natural numbers

Ex. 5.60 | Q 49 | Page 53

Find the sum of first n odd natural numbers

Ex. 5.60 | Q 50.1 | Page 53

Find the sum of the odd numbers between 0 and 50.

Ex. 5.60 | Q 50.1 | Page 53

Find the sum of the odd numbers between 0 and 50.

Ex. 5.60 | Q 50.2 | Page 53

Find the sum of all odd numbers between 100 and 200.

Ex. 5.60 | Q 50.2 | Page 53

Find the sum of all odd numbers between 100 and 200.

Ex. 5.60 | Q 51 | Page 53

Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.

Ex. 5.60 | Q 51 | Page 53

Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.

Ex. 5.60 | Q 52 | Page 53

Find the sum of all integers between 84 and 719, which are multiples of 5.

Ex. 5.60 | Q 52 | Page 53

Find the sum of all integers between 84 and 719, which are multiples of 5.

Ex. 5.60 | Q 53 | Page 53

Find the sum of all integers between 50 and 500, which are divisible by 7.

Ex. 5.60 | Q 53 | Page 53

Find the sum of all integers between 50 and 500, which are divisible by 7.

Ex. 5.60 | Q 54 | Page 53

Find the sum of all even integers between 101 and 999.

Ex. 5.60 | Q 54 | Page 53

Find the sum of all even integers between 101 and 999.

Ex. 5.60 | Q 55 | Page 53

Find the sum of all integers between 100 and 550, which are divisible by 9.

Ex. 5.60 | Q 55 | Page 53

Find the sum of all integers between 100 and 550, which are divisible by 9.

Ex. 5.60 | Q 56.1 | Page 53

Let there be an A.P. with the first term ‘a’, common difference’. If a denotes its nth term and Sn the sum of first n terms, find

n and Sn, if a = 5, d = 3 and an = 50.

Ex. 5.60 | Q 56.1 | Page 53

Let there be an A.P. with the first term ‘a’, common difference’. If a denotes its nth term and Sn the sum of first n terms, find

n and Sn, if a = 5, d = 3 and an = 50.

Ex. 5.60 | Q 56.2 | Page 53

Let there be an A.P. with the first term 'a', common difference'. If an a denotes in nth term and Sn the sum of first n terms, find.

n and a, if an = 4, d = 2 and Sn = −14.

Ex. 5.60 | Q 56.2 | Page 53

Let there be an A.P. with the first term 'a', common difference'. If an a denotes in nth term and Sn the sum of first n terms, find.

n and a, if an = 4, d = 2 and Sn = −14.

Ex. 5.60 | Q 56.3 | Page 53

Let there be an A.P. with the first term 'a', common difference 'd'. If an a denotes in nth term and Sn the sum of first n terms, find.

d, if a = 3, n = 8 and Sn = 192.

Ex. 5.60 | Q 56.3 | Page 53

Let there be an A.P. with the first term 'a', common difference 'd'. If an a denotes in nth term and Sn the sum of first n terms, find.

d, if a = 3, n = 8 and Sn = 192.

Ex. 5.60 | Q 56.4 | Page 53

Let there be an A.P. with the first term ‘a’, common difference 'd’. If a denotes its nth term and Sn the sum of first n terms, find.

a, if an = 28, Sn = 144 and n= 9.

Ex. 5.60 | Q 56.4 | Page 53

Let there be an A.P. with the first term ‘a’, common difference 'd’. If a denotes its nth term and Sn the sum of first n terms, find.

a, if an = 28, Sn = 144 and n= 9.

Ex. 5.60 | Q 56.5 | Page 53

Let there be an A.P. with the first term 'a', common difference 'd'. If an a denotes in nth term and Sn the sum of first n terms, find.

n and d, if a = 8, an = 62 and Sn = 210

Ex. 5.60 | Q 56.5 | Page 53

Let there be an A.P. with the first term 'a', common difference 'd'. If an a denotes in nth term and Sn the sum of first n terms, find.

n and d, if a = 8, an = 62 and Sn = 210

Ex. 5.60 | Q 56.6 | Page 53

Let there be an A.P. with the first term 'a', common difference 'd'. If an a denotes in nth term and Sn the sum of first n terms, find.

n and an, if a= 2, d = 8 and Sn = 90.

Ex. 5.60 | Q 56.6 | Page 53

Let there be an A.P. with the first term 'a', common difference 'd'. If an a denotes in nth term and Sn the sum of first n terms, find.

n and an, if a= 2, d = 8 and Sn = 90.

Ex. 5.60 | Q 56.7 | Page 53

Let there be an A.P. with first term 'a', common difference 'd'. If an denotes in nth term and Sn the sum of first n terms, find.

\[k, \text{ if }  S_n = 3 n^2 + 5n \text{ and }  a_k = 164\]

 

Ex. 5.60 | Q 56.7 | Page 53

Let there be an A.P. with first term 'a', common difference 'd'. If an denotes in nth term and Sn the sum of first n terms, find.

\[k, \text{ if }  S_n = 3 n^2 + 5n \text{ and }  a_k = 164\]

 

Ex. 5.60 | Q 56.8 | Page 53

Find the sum of first 22 terms of an A.P. in which d = 22 and a = 149.

Ex. 5.60 | Q 56.8 | Page 53

Find the sum of first 22 terms of an A.P. in which d = 22 and a = 149.

Ex. 5.60 | Q 57 | Page 54

If Sn denotes the sum of first n terms of an A.P., prove that S12 = 3(S8 − S4).

 
Ex. 5.60 | Q 57 | Page 54

If Sn denotes the sum of first n terms of an A.P., prove that S12 = 3(S8 − S4).

 
Ex. 5.60 | Q 61 | Page 54

In a school, students decided to plant trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be double of the class in which they are studying. If there are 1 to 12 classes in the school and each class has two sections, find how many trees were planted by the students.

Ex. 5.60 | Q 61 | Page 54

In a school, students decided to plant trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be double of the class in which they are studying. If there are 1 to 12 classes in the school and each class has two sections, find how many trees were planted by the students.

Ex. 5.60 | Q 62 | Page 54

Ramkali would need ₹1800 for admission fee and books etc., for her daughter to start going to school from next year. She saved ₹50 in the first month of this year and increased her monthly saving by ₹20. After a year, how much money will she save? Will she be able to fulfil her dream of sending her daughter to school?

Ex. 5.60 | Q 62 | Page 54

Ramkali would need ₹1800 for admission fee and books etc., for her daughter to start going to school from next year. She saved ₹50 in the first month of this year and increased her monthly saving by ₹20. After a year, how much money will she save? Will she be able to fulfil her dream of sending her daughter to school?

Ex. 5.60 | Q 63 | Page 54

A man saved Rs 16500 in ten years. In each year after the first, he saved Rs 100 more than he did in the preceding year. How much did he save in the first year?

Ex. 5.60 | Q 64 | Page 54

A man saved Rs. 32 during the first year, Rs 36 in the second year and in this way he increases his saving by Rs 4 every year. Find in what time his saving will be Rs. 200.

Ex. 5.60 | Q 65 | Page 54

A man arranges to pay off a debt of Rs 3600 by 40 annual instalments which form an arithmetic series. When 30 of the instalments are paid, he dies leaving one-third of all debt unpaid, finds the value of the first instalment.

Ex. 5.60 | Q 66 | Page 54

There are 25 trees at equal distances of 5 metres in a line with a well, the distance of the well from the nearest tree being 10 metres. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. Find the total distance the gardener will cover in order to water all the trees.

Ex. 5.60 | Q 66 | Page 54

There are 25 trees at equal distances of 5 metres in a line with a well, the distance of the well from the nearest tree being 10 metres. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. Find the total distance the gardener will cover in order to water all the trees.

Ex. 5.60 | Q 67 | Page 54

A man is employed to count Rs 10710. He counts at the rate of Rs 180 per minute for half an hour. After this he counts at the rate of Rs 3 less every minute than the preceding minute. Find the time taken by him to count the entire amount.

Ex. 5.60 | Q 67 | Page 54

A man is employed to count Rs 10710. He counts at the rate of Rs 180 per minute for half an hour. After this he counts at the rate of Rs 3 less every minute than the preceding minute. Find the time taken by him to count the entire amount.

Ex. 5.60 | Q 68 | Page 54

A piece of equipment cost a certain factory Rs 60,000. If it depreciates in value, 15% the first, 13.5% the next year, 12% the third year, and so on. What will be its value at the end of 10 years, all percentages applying to the original cost?

Ex. 5.60 | Q 68 | Page 54

A piece of equipment cost a certain factory Rs 60,000. If it depreciates in value, 15% the first, 13.5% the next year, 12% the third year, and so on. What will be its value at the end of 10 years, all percentages applying to the original cost?

Ex. 5.60 | Q 69 | Page 55

A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes.

Ex. 5.60 | Q 69 | Page 55

A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes.

Ex. 5.60 | Q 70 | Page 55

If Sn denotes the sum of the first n terms of an A.P., prove that S30 = 3(S20 − S10)

 
Ex. 5.60 | Q 70 | Page 55

If Sn denotes the sum of the first n terms of an A.P., prove that S30 = 3(S20 − S10)

 
Ex. 5.60 | Q 71 | Page 55

x is nth term of the given A.P. an = x find x .

Ex. 5.60 | Q 71 | Page 55

x is nth term of the given A.P. an = x find x .

Chapter 5: Arithmetic Progression solutions [Page 56]

Q 1 | Page 56

Define an arithmetic progression.

 
Q 1 | Page 56

Define an arithmetic progression.

 
Q 2 | Page 56

Write the common difference of an A.P. whose nth term is an = 3n + 7.

 
Q 2 | Page 56

Write the common difference of an A.P. whose nth term is an = 3n + 7.

 
Q 3 | Page 56

Which term of the sequence 114, 109, 104, ... is the first negative term?

 
Q 3 | Page 56

Which term of the sequence 114, 109, 104, ... is the first negative term?

 
Q 4 | Page 56

Write the value of a30 − a10 for the A.P. 4, 9, 14, 19, ....

 
Q 4 | Page 56

Write the value of a30 − a10 for the A.P. 4, 9, 14, 19, ....

 
Q 5 | Page 56

Write 5th term from the end of the A.P. 3, 5, 7, 9, ..., 201.

 
Q 5 | Page 56

Write 5th term from the end of the A.P. 3, 5, 7, 9, ..., 201.

 
Q 6 | Page 56

Write the value of x for which 2xx + 10 and 3x + 2 are in A.P.

 
Q 6 | Page 56

Write the value of x for which 2xx + 10 and 3x + 2 are in A.P.

 
Q 7 | Page 56

Write the nth term of an A.P. the sum of whose n terms is Sn.

 
Q 7 | Page 56

Write the nth term of an A.P. the sum of whose n terms is Sn.

 
Q 8 | Page 56

Write the sum of first n odd natural numbers.

 
Q 8 | Page 56

Write the sum of first n odd natural numbers.

 
Q 9 | Page 56

Write the sum of first n even natural numbers.

 
Q 9 | Page 56

Write the sum of first n even natural numbers.

 
Q 10 | Page 56

If the sum of n terms of an A.P. is Sn = 3n2 + 5n. Write its common difference.

 
Q 10 | Page 56

If the sum of n terms of an A.P. is Sn = 3n2 + 5n. Write its common difference.

 
Q 11 | Page 56

Write the expression of the common difference of an A.P. whose first term is a and nth term is b.

Q 11 | Page 56

Write the expression of the common difference of an A.P. whose first term is a and nth term is b.

Q 12 | Page 56

The first term of an A.P. is p and its common difference is q. Find its 10th term.

 
Q 12 | Page 56

The first term of an A.P. is p and its common difference is q. Find its 10th term.

 
Q 13 | Page 56

For what value of p are 2p + 1, 13, 5p − 3 are three consecutive terms of an A.P.?

 
Q 13 | Page 56

For what value of p are 2p + 1, 13, 5p − 3 are three consecutive terms of an A.P.?

 
Q 14 | Page 56

If `4/5` , a, 2 are three consecutive terms of an A.P., then find the value of a

Q 14 | Page 56

If `4/5` , a, 2 are three consecutive terms of an A.P., then find the value of a

Q 15 | Page 56

If the sum of first p term of an A.P. is ap2 + bp, find its common difference.

 
Q 15 | Page 56

If the sum of first p term of an A.P. is ap2 + bp, find its common difference.

 
Q 17 | Page 56

The given terms are 2k + 1, 3k + 3 and 5k − 1. find AP.

Q 17 | Page 56

The given terms are 2k + 1, 3k + 3 and 5k − 1. find AP.

Q 18 | Page 56

Write the nth term of the \[A . P . \frac{1}{m}, \frac{1 + m}{m}, \frac{1 + 2m}{m}, . . . .\]

 
Q 18 | Page 56

Write the nth term of the \[A . P . \frac{1}{m}, \frac{1 + m}{m}, \frac{1 + 2m}{m}, . . . .\]

 

Chapter 5: Arithmetic Progression solutions [Pages 57 - 60]

Q 1 | Page 57

Mark the correct alternative in each of the following:
If 7th and 13th terms of an A.P. be 34 and 64 respectively, then its 18th term is

  • 87

  • 88

  •  89

  • 90

Q 1 | Page 57

Mark the correct alternative in each of the following:
If 7th and 13th terms of an A.P. be 34 and 64 respectively, then its 18th term is

  • 87

  • 88

  •  89

  • 90

Q 2 | Page 57

If the sum of P terms of an A.P. is q and the sum of q terms is p, then the sum of p + qterms will be

  • 0

  • p − q

  •  q

  • −(p + q)

Q 2 | Page 57

If the sum of P terms of an A.P. is q and the sum of q terms is p, then the sum of p + qterms will be

  • 0

  • p − q

  •  q

  • −(p + q)

Q 3 | Page 57

If the sum of n terms of an A.P. be 3n2 + n and its common difference is 6, then its first term is

  • 2

  • 3

  • 1

  • 4

Q 3 | Page 57

If the sum of n terms of an A.P. be 3n2 + n and its common difference is 6, then its first term is

  • 2

  • 3

  • 1

  • 4

Q 4 | Page 57

The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be

  • 5

  • 6

  • 7

  • 8

Q 4 | Page 57

The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be

  • 5

  • 6

  • 7

  • 8

Q 5 | Page 57

If the sum of n terms of an A.P. is 3n2 + 5n then which of its terms is 164?

  •  26th

  •  27th

  •  28th

  • none of these.

Q 5 | Page 57

If the sum of n terms of an A.P. is 3n2 + 5n then which of its terms is 164?

  •  26th

  •  27th

  •  28th

  • none of these.

Q 6 | Page 57

If the sum of n terms of an A.P. is 2n2 + 5n, then its nth term is

  • 4n − 3

  • 3n − 4

  • 4n + 3

  • 3n + 4

Q 6 | Page 57

If the sum of n terms of an A.P. is 2n2 + 5n, then its nth term is

  • 4n − 3

  • 3n − 4

  • 4n + 3

  • 3n + 4

Q 7 | Page 57

If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is

  •  13

  • 9

  •  21

  • 17

Q 7 | Page 57

If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is

  •  13

  • 9

  •  21

  • 17

Q 8 | Page 57

If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times, the least, then the numbers are

  • 5, 10, 15, 20

  • 4, 101, 16, 22

  • 3, 7, 11, 15

  •  none of these

Q 8 | Page 57

If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times, the least, then the numbers are

  • 5, 10, 15, 20

  • 4, 101, 16, 22

  • 3, 7, 11, 15

  •  none of these

Q 9 | Page 57

Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by Sn − kSn−1 + Sn−2, then k =

  • 1

  • 2

  • 3

  • none of these.

Q 9 | Page 57

Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by Sn − kSn−1 + Sn−2, then k =

  • 1

  • 2

  • 3

  • none of these.

Q 10 | Page 57

The first and last term of an A.P. are a and l respectively. If S is the sum of all the terms of the A.P. and the common difference is given by \[\frac{l^2 - a^2}{k - (l + a)}\] , then k =

 

 

Q 10 | Page 57

The first and last term of an A.P. are a and l respectively. If S is the sum of all the terms of the A.P. and the common difference is given by \[\frac{l^2 - a^2}{k - (l + a)}\] , then k =

 

 

Q 11 | Page 57

If the sum of first n even natural numbers is equal to times the sum of first n odd natural numbers, then k =

  • \[\frac{1}{n}\]
     
  • \[\frac{n - 1}{n}\]
     
  • \[\frac{n + 1}{2n}\]
     
  • \[\frac{n + 1}{n}\]
     
Q 11 | Page 57

If the sum of first n even natural numbers is equal to times the sum of first n odd natural numbers, then k =

  • \[\frac{1}{n}\]
     
  • \[\frac{n - 1}{n}\]
     
  • \[\frac{n + 1}{2n}\]
     
  • \[\frac{n + 1}{n}\]
     
Q 12 | Page 57

If the first, second and last term of an A.P. are ab and 2a respectively, its sum is

  • \[\frac{ab}{2(b - a)}\]

     

  • \[\frac{ab}{(b - a)}\]

     

  • \[\frac{3ab}{2(b - a)}\]

     

  •  none of these 

Q 12 | Page 57

If the first, second and last term of an A.P. are ab and 2a respectively, its sum is

  • \[\frac{ab}{2(b - a)}\]

     

  • \[\frac{ab}{(b - a)}\]

     

  • \[\frac{3ab}{2(b - a)}\]

     

  •  none of these 

Q 13 | Page 58

If S1 is the sum of an arithmetic progression of 'n' odd number of terms and S2 the sum of the terms of the series in odd places, then \[\frac{S_1}{S_2} =\]

 

  • \[\frac{2n}{n + 1}\]

     

  • \[\frac{n}{n + 1}\]

     

  • \[\frac{n + 1}{2n}\]

     

  • \[\frac{n + 1}{n}\]

     

Q 13 | Page 58

If S1 is the sum of an arithmetic progression of 'n' odd number of terms and S2 the sum of the terms of the series in odd places, then \[\frac{S_1}{S_2} =\]

 

  • \[\frac{2n}{n + 1}\]

     

  • \[\frac{n}{n + 1}\]

     

  • \[\frac{n + 1}{2n}\]

     

  • \[\frac{n + 1}{n}\]

     

Q 14 | Page 58

If in an A.P. Sn = n2p and Sm = m2p, where Sr denotes the sum of r terms of the A.P., then Sp is equal to 

  • \[\frac{1}{2} p^3\]

     

  • m n p

  •  p3

  • (m + np2

Q 14 | Page 58

If in an A.P. Sn = n2p and Sm = m2p, where Sr denotes the sum of r terms of the A.P., then Sp is equal to 

  • \[\frac{1}{2} p^3\]

     

  • m n p

  •  p3

  • (m + np2

Q 15 | Page 58

If Sn denote the sum of the first terms of an A.P. If S2n = 3Sn, then S3n : Sn is equal to

  • 4

  • 6

  • 8

  • 10

Q 15 | Page 58

If Sn denote the sum of the first terms of an A.P. If S2n = 3Sn, then S3n : Sn is equal to

  • 4

  • 6

  • 8

  • 10

Q 16 | Page 58

In an AP. Sp = q, Sq = p and Sr denotes the sum of first r terms. Then, Sp+q is equal to

  • 0

  • −(p + q)

  •  p + q

  • pq

Q 16 | Page 58

In an AP. Sp = q, Sq = p and Sr denotes the sum of first r terms. Then, Sp+q is equal to

  • 0

  • −(p + q)

  •  p + q

  • pq

Q 17 | Page 58

If Sr denotes the sum of the first r terms of an A.P. Then , S3n: (S2n − Sn) is

  • n

  • 3n

  • 3

  • none of these

Q 17 | Page 58

If Sr denotes the sum of the first r terms of an A.P. Then , S3n: (S2n − Sn) is

  • n

  • 3n

  • 3

  • none of these

Q 18 | Page 58

If the first term of an A.P. is 2 and common difference is 4, then the sum of its 40 terms is 

  • 3200

  • 1600

  •  200

  •  2800

Q 18 | Page 58

If the first term of an A.P. is 2 and common difference is 4, then the sum of its 40 terms is 

  • 3200

  • 1600

  •  200

  •  2800

Q 19 | Page 58

The number of terms of the A.P. 3, 7, 11, 15, ... to be taken so that the sum is 406 is

  • 5

  • 10

  • 12

  • 14

  • 20

Q 19 | Page 58

The number of terms of the A.P. 3, 7, 11, 15, ... to be taken so that the sum is 406 is

  • 5

  • 10

  • 12

  • 14

  • 20

Q 20 | Page 58

Sum of n terms of the series  \[\sqrt{2} + \sqrt{8} + \sqrt{18} + \sqrt{32} + . . \text{ is } \]

 

  • \[\frac{n (n + 1)}{2}\]

     

  • \[2n (n + 1)\]

     

  • \[\frac{n (n + 1)}{\sqrt{2}}\]

     

  • 1

Q 20 | Page 58

Sum of n terms of the series  \[\sqrt{2} + \sqrt{8} + \sqrt{18} + \sqrt{32} + . . \text{ is } \]

 

  • \[\frac{n (n + 1)}{2}\]

     

  • \[2n (n + 1)\]

     

  • \[\frac{n (n + 1)}{\sqrt{2}}\]

     

  • 1

Q 21 | Page 58

The 9th term of an A.P. is 449 and 449th term is 9. The term which is equal to zero is

  • 501th

  • 502th

  • 508th

  • none of these

Q 21 | Page 58

The 9th term of an A.P. is 449 and 449th term is 9. The term which is equal to zero is

  • 501th

  • 502th

  • 508th

  • none of these

Q 22 | Page 58

If \[\frac{1}{x + 2}, \frac{1}{x + 3}, \frac{1}{x + 5}\]  are in A.P. Then, x =

  • 5

  • 3

  • 1

  • 2

Q 22 | Page 58

If \[\frac{1}{x + 2}, \frac{1}{x + 3}, \frac{1}{x + 5}\]  are in A.P. Then, x =

  • 5

  • 3

  • 1

  • 2

Q 23 | Page 58

The nth term of an A.P., the sum of whose n terms is Sn, is

  •  Sn + Sn−1

  • Sn − Sn−1

  • Sn + Sn+1

  • Sn − Sn+1

Q 23 | Page 58

The nth term of an A.P., the sum of whose n terms is Sn, is

  •  Sn + Sn−1

  • Sn − Sn−1

  • Sn + Sn+1

  • Sn − Sn+1

Q 24 | Page 58

The common difference of an A.P., the sum of whose n terms is Sn, is

  • Sn − 2Sn−1 + Sn−2

  • Sn − 2Sn−1 − Sn−2

  • Sn − Sn−2

  •  Sn − Sn−1

Q 24 | Page 58

The common difference of an A.P., the sum of whose n terms is Sn, is

  • Sn − 2Sn−1 + Sn−2

  • Sn − 2Sn−1 − Sn−2

  • Sn − Sn−2

  •  Sn − Sn−1

Q 25 | Page 58

If the sums of n terms of two arithmetic progressions are in the ratio \[\frac{3n + 5}{5n - 7}\] , then their nth terms are in the ratio

  
  • \[\frac{3n - 1}{5n - 1}\]

     

  • \[\frac{3n + 1}{5n + 1}\]

     

  • \[\frac{5n + 1}{3n + 1}\]

     

  • \[\frac{5n - 1}{3n - 1}\]

     

Q 25 | Page 58

If the sums of n terms of two arithmetic progressions are in the ratio \[\frac{3n + 5}{5n - 7}\] , then their nth terms are in the ratio

  
  • \[\frac{3n - 1}{5n - 1}\]

     

  • \[\frac{3n + 1}{5n + 1}\]

     

  • \[\frac{5n + 1}{3n + 1}\]

     

  • \[\frac{5n - 1}{3n - 1}\]

     

Q 26 | Page 59

If Sn denote the sum of n terms of an A.P. with first term and common difference dsuch that \[\frac{Sx}{Skx}\]  is independent of x, then

 

  •  da

  • d = 2a

  • a = 2d

  • = −a

Q 26 | Page 59

If Sn denote the sum of n terms of an A.P. with first term and common difference dsuch that \[\frac{Sx}{Skx}\]  is independent of x, then

 

  •  da

  • d = 2a

  • a = 2d

  • = −a

Q 27 | Page 59

If the first term of an A.P. is a and nth term is b, then its common difference is

  • \[\frac{b - a}{n + 1}\]

     

  • \[\frac{b - a}{n - 1}\]

     

  • \[\frac{b - a}{n}\]

     

  • \[\frac{b + a}{n - 1}\]

     

Q 27 | Page 59

If the first term of an A.P. is a and nth term is b, then its common difference is

  • \[\frac{b - a}{n + 1}\]

     

  • \[\frac{b - a}{n - 1}\]

     

  • \[\frac{b - a}{n}\]

     

  • \[\frac{b + a}{n - 1}\]

     

Q 28 | Page 59

The sum of first n odd natural numbers is

  •  2n − 1

  •  2n + 1

  •  n2

  •  n2 − 1

Q 28 | Page 59

The sum of first n odd natural numbers is

  •  2n − 1

  •  2n + 1

  •  n2

  •  n2 − 1

Q 29 | Page 59

Two A.P.'s have the same common difference. The first term of one of these is 8 and that of the other is 3. The difference between their 30th term is

  • 11

  • 3

  • 8

  • 5

Q 29 | Page 59

Two A.P.'s have the same common difference. The first term of one of these is 8 and that of the other is 3. The difference between their 30th term is

  • 11

  • 3

  • 8

  • 5

Q 30 | Page 59

If 18, ab, −3 are in A.P., the a + b =

  •  19

  • 7

  • 11

  • 15

Q 30 | Page 59

If 18, ab, −3 are in A.P., the a + b =

  •  19

  • 7

  • 11

  • 15

Q 31 | Page 59

The sum of n terms of two A.P.'s are in the ratio 5n + 9 : 9n + 6. Then, the ratio of their 18th term is

  • \[\frac{179}{321}\]

     

  • \[\frac{178}{321}\]

     

  • \[\frac{175}{321}\]

     

  • \[\frac{176}{321}\]

     

  • non above these

Q 31 | Page 59

The sum of n terms of two A.P.'s are in the ratio 5n + 9 : 9n + 6. Then, the ratio of their 18th term is

  • \[\frac{179}{321}\]

     

  • \[\frac{178}{321}\]

     

  • \[\frac{175}{321}\]

     

  • \[\frac{176}{321}\]

     

  • non above these

Q 32 | Page 59

If \[\frac{5 + 9 + 13 + . . . \text{ to n terms} }{7 + 9 + 11 + . . . \text{ to (n + 1) terms}} = \frac{17}{16},\] then n =

 

  • 8

  • 7

  • 10

  • 11

Q 32 | Page 59

If \[\frac{5 + 9 + 13 + . . . \text{ to n terms} }{7 + 9 + 11 + . . . \text{ to (n + 1) terms}} = \frac{17}{16},\] then n =

 

  • 8

  • 7

  • 10

  • 11

Q 33 | Page 59

The sum of n terms of an A.P. is 3n2 + 5n, then 164 is its

  •  24th term

  •  27th term

  • 26th term

  •  25th term

Q 33 | Page 59

The sum of n terms of an A.P. is 3n2 + 5n, then 164 is its

  •  24th term

  •  27th term

  • 26th term

  •  25th term

Q 34 | Page 59

If the nth term of an A.P. is 2n + 1, then the sum of first n terms of the A.P. is 

  • n(n − 2)

  • n(n + 2)

  • n(n + 1)

  •  n(n − 1)

Q 34 | Page 59

If the nth term of an A.P. is 2n + 1, then the sum of first n terms of the A.P. is 

  • n(n − 2)

  • n(n + 2)

  • n(n + 1)

  •  n(n − 1)

Q 35 | Page 59

If 18th and 11th term of an A.P. are in the ratio 3 : 2, then its 21st and 5th terms are in the ratio

  •  3 : 2

  •  3 : 1

  • 1 : 3

  • 2 : 3

Q 35 | Page 59

If 18th and 11th term of an A.P. are in the ratio 3 : 2, then its 21st and 5th terms are in the ratio

  •  3 : 2

  •  3 : 1

  • 1 : 3

  • 2 : 3

Q 36 | Page 59

The sum of first 20 odd natural numbers is

  • 100

  • 210

  • 400

  • 420

Q 36 | Page 59

The sum of first 20 odd natural numbers is

  • 100

  • 210

  • 400

  • 420

Q 37 | Page 59

The common difference of the A.P. is \[\frac{1}{2q}, \frac{1 - 2q}{2q}, \frac{1 - 4q}{2q}, . . .\] is 

 
  • −1

  • 1

  • q

  • 2q

Q 37 | Page 59

The common difference of the A.P. is \[\frac{1}{2q}, \frac{1 - 2q}{2q}, \frac{1 - 4q}{2q}, . . .\] is 

 
  • −1

  • 1

  • q

  • 2q

Q 38 | Page 59

The common difference of the A.P.

\[\frac{1}{3}, \frac{1 - 3b}{3}, \frac{1 - 6b}{3}, . . .\] is 
 
  • \[\frac{1}{3}\]

     

  • \[- \frac{1}{3}\]

     

  • b

  • b

Q 38 | Page 59

The common difference of the A.P.

\[\frac{1}{3}, \frac{1 - 3b}{3}, \frac{1 - 6b}{3}, . . .\] is 
 
  • \[\frac{1}{3}\]

     

  • \[- \frac{1}{3}\]

     

  • b

  • b

Q 39 | Page 59

The common difference of the A.P. \[\frac{1}{2b}, \frac{1 - 6b}{2b}, \frac{1 - 12b}{2b}, . . .\] is 

 
  •  2b

  • −2b

  • 3

  •  - 3 

Q 39 | Page 59

The common difference of the A.P. \[\frac{1}{2b}, \frac{1 - 6b}{2b}, \frac{1 - 12b}{2b}, . . .\] is 

 
  •  2b

  • −2b

  • 3

  •  - 3 

Q 40 | Page 60

If k, 2k − 1 and 2k + 1 are three consecutive terms of an A.P., the value of k is

  •  −2

  • 3

  • - 3 

  • 6

Q 40 | Page 60

If k, 2k − 1 and 2k + 1 are three consecutive terms of an A.P., the value of k is

  •  −2

  • 3

  • - 3 

  • 6

Q 41 | Page 60

The next term of the A.P.  \[\sqrt{7}, \sqrt{28}, \sqrt{63}, . . . .\]

 
  • \[\sqrt{70}\]

     

  • \[\sqrt{84}\]

     

  • \[\sqrt{97}\]

     

  • \[\sqrt{112}\]

     

Q 41 | Page 60

The next term of the A.P.  \[\sqrt{7}, \sqrt{28}, \sqrt{63}, . . . .\]

 
  • \[\sqrt{70}\]

     

  • \[\sqrt{84}\]

     

  • \[\sqrt{97}\]

     

  • \[\sqrt{112}\]

     

Q 42 | Page 60

The first three terms of an A.P. respectively are 3y − 1, 3y + 5 and 5y + 1. Then, y equals

  • - 3 

  • 4

  • 5

  • 2

Q 42 | Page 60

The first three terms of an A.P. respectively are 3y − 1, 3y + 5 and 5y + 1. Then, y equals

  • - 3 

  • 4

  • 5

  • 2

Chapter 5: Arithmetic Progression

Ex. 5.10Ex. 5.20Ex. 5.30Ex. 5.40Ex. 5.50Ex. 5.60Others

RD Sharma 10 Mathematics

10 Mathematics - Shaalaa.com

RD Sharma solutions for Class 10 Mathematics chapter 5 - Arithmetic Progression

RD Sharma solutions for Class 10 Maths chapter 5 (Arithmetic Progression) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE 10 Mathematics solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com are providing such solutions so that students can prepare for written exams. RD Sharma textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 10 Mathematics chapter 5 Arithmetic Progression are Introduction to Sequence, Arithmetic Progression Examples and Solutions, Terms in a sequence, Geometric Mean, Arithmetic Progression, Geometric Progression, General Term of an Arithmetic Progression, General Term of an Geomatric Progression, Sum of First n Terms of an AP, Sum of the First 'N' Terms of an Geometric Progression, Arithmetic Mean, Sum of First n Terms of an AP, Derivation of the n th Term, Application in Solving Daily Life Problems, Arithmetic Progressions Examples and Solutions, Arithmetic Progression, General Term of an Arithmetic Progression, nth Term of an AP.

Using RD Sharma Class 10 solutions Arithmetic Progression exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in RD Sharma Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 10 prefer RD Sharma Textbook Solutions to score more in exam.

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