#### Chapters

Chapter 2: Polynomials

Chapter 3: Pair of Linear Equations in Two Variables

Chapter 4: Triangles

Chapter 5: Trigonometric Ratios

Chapter 6: Trigonometric Identities

Chapter 7: Statistics

Chapter 8: Quadratic Equations

Chapter 9: Arithmetic Progression

Chapter 10: Circles

Chapter 11: Constructions

Chapter 12: Trigonometry

Chapter 13: Probability

Chapter 14: Co-Ordinate Geometry

Chapter 15: Areas Related to Circles

Chapter 16: Surface Areas and Volumes

#### RD Sharma 10 Mathematics

## Chapter 9 : Arithmetic Progression

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

a_{n} = 3n + 2

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

a_{n} = 3n + 2

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

`a_n = (n - 3)/3`

Write the first five terms of the following sequences whose *n*th terms are:

`a_n = 3^n`

Write the first five terms of the following sequences whose *n*th terms are:

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

Write the first five terms of the following sequences whose *n*th terms are:

a_{n} = (−1)^{n} 2^{n}

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

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

Write the first five terms of the following sequences whose *n*th terms are:

a_{n} = n^{2} − n + 1

Write the first five terms of the following sequences whose *n*th terms are:

a_{n} = 2n^{2} − 3n + 1

Write the first five terms of the following sequences whose *n*th terms are:

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

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

a_{n} = 5n - 4; a_{12} and a_{15}

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`

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

a_{n} = n (n −1) (n − 2); a_{5} and a_{8}

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

a_{n} = (n − 1) (2 − n) (3 + n); a_{1}, a_{2}, a_{3}

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

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

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

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

Find the next five terms of the following sequences given by

a_{1} = a_{2} = 2, a_{n} = a_{n−1} − 3, n > 2

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

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

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

a_{1} = 4, a_{n} = 4a_{n−1} + 3, n > 1.

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

−5, −1, 3, 7, ...

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

−5, −1, 3, 7, ...

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

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

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

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

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

0.3, 0.55, 0.80, 1.05, ...

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

0.3, 0.55, 0.80, 1.05, ...

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

−1.1, −3.1, −5.1, −7.1, ...

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

−1.1, −3.1, −5.1, −7.1, ...

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

a = 4,d = -3

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

a = 4,d = -3

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

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

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

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

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

a = -1.5, d = -0.5

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

a = -1.5, d = -0.5

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.

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.

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.

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.

Show that the sequence defined by *a _{n}* = 5

*n*−7 is an A.P, find its common difference.

Show that the sequence defined by *a _{n}* = 5

*n*−7 is an A.P, find its common difference.

Show that the sequence defined by a_{n} = 3n^{2} − 5 is not an A.P

Show that the sequence defined by a_{n} = 3n^{2} − 5 is not an A.P

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

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

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

1, −2, −5, −8, ...

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

1, −2, −5, −8, ...

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

0, −3, −6, −9, ...

0, −3, −6, −9, ...

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

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

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

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

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

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

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

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

Write the sequence with *n*th term:

a_{n} = 3 + 4n

Write the sequence with *n*th term:

a_{n} = 3 + 4n

Write the sequence with nth term *a*_{n} = 5 + 2*n*

Write the sequence with nth term *a*_{n} = 5 + 2*n*

Write the sequence with *n*th term a_{n} = 6 − n

Write the sequence with *n*th term a_{n} = 6 − n

Write the sequence with *n*th term: a_{n} = 9 − 5n

Write the sequence with *n*th term: a_{n} = 9 − 5n

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

3, 6, 12, 24, ...

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

3, 6, 12, 24, ...

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

0, −4, −8, −12, ...

0, −4, −8, −12, ...

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 ......`

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 ......`

12, 2, −8, −18, ...

12, 2, −8, −18, ...

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

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

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

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

1.0, 1.7, 2.4, 3.1, ...

1.0, 1.7, 2.4, 3.1, ...

−225, −425, −625, −825, ...

−225, −425, −625, −825, ...

10, 10 + 2^{5}, 10 + 2^{6}, 10 + 2^{7},...

10, 10 + 2^{5}, 10 + 2^{6}, 10 + 2^{7},...

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

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

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

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

Find the n^{th} term of the A.P. 13, 8, 3, −2, ...

Find the n^{th} term of the A.P. 13, 8, 3, −2, ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

7, 10, 13, ... 43.

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

7, 10, 13, ... 43.

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

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

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

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

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

How many terms are there in the AP?

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

How many terms are there in the AP?

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

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

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

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

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

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

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

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.

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.

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

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

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

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.

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.

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.

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.

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

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

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

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

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

3, 8, 13, ..., 253

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

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

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

Find the second term and n^{th} term of an A.P. whose 6^{th} term is 12 and 8^{th} term is 22.

How many numbers of two digit are divisible by 3?

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

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

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

Find a_{30} − a_{20} for the A.P.

−9, −14, −19, −24, ...

Find a_{30} − a_{20} for the A.P.

−9, −14, −19, −24, ...

Find a_{30} − a_{20} for the A.P.

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

Find a_{30} − a_{20} for the A.P.

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

Write the expression a_{n}- a_{k} for the A.P. a, a + d, a + 2d, ... Hence, find the common difference of the A.P. for which

11^{th} term is 5 and the 13^{th} term is 79.

Write the expression a_{n}- a_{k} for the A.P. a, a + d, a + 2d, ... Hence, find the common difference of the A.P. for which

11^{th} term is 5 and the 13^{th} term is 79.

Write the expression a_{n}- a_{k} for the A.P. a, a + d, a + 2d, ... Hence, find the common difference of the A.P. for which a_{10} −a_{5}_{ }= 200

Write the expression a_{n}- a_{k} for the A.P. a, a + d, a + 2d, ... Hence, find the common difference of the A.P. for which a_{10} −a_{5}_{ }= 200

Write the expression a_{n}- a_{k} for the A.P. a, a + d, a + 2d, ... Hence, find the common difference of the A.P. for which

20^{th} term is 10 more than the 18^{th} term.

_{n}- a_{k} for the A.P. a, a + d, a + 2d, ... Hence, find the common difference of the A.P. for which

20^{th} term is 10 more than the 18^{th} term.

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

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

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

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

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

−1, −3, −5, −7, ...; x = −151

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

−1, −3, −5, −7, ...; x = −151

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

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

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`

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`

If an A.P. consists of *n* terms with first term a and *n*^{th} term *l *show that the sum of the m^{th} term from the beginning and the m^{th} term from the end is (a + l).

If an A.P. consists of *n* terms with first term a and *n*^{th} term *l *show that the sum of the m^{th} term from the beginning and the m^{th} term from the end is (a + l).

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

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

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

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

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

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

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

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

For what value of *n*, are the n^{th} terms of two APs 63, 65, 67, and 3, 10, 17, … equal?

How many multiples of 4 lie between 10 and 250?

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

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

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

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

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

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

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.

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

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.

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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.

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.

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

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

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

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

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

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

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

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

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

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

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

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

Show that (a − b)^{2}, (a^{2} + b^{2}) and (a + b)^{2} are in A.P.

Show that (a − b)^{2}, (a^{2} + b^{2}) and (a + b)^{2} are in A.P.

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

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

Find the sum of the following arithmetic progressions:

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

Find the sum of the following arithmetic progressions:

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

Find the sum of the following arithmetic progressions:

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

Find the sum of the following arithmetic progressions:

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

Find the sum of the following arithmetic progressions:

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

Find the sum of the following arithmetic progressions:

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

Find the sum of the following arithmetic progressions:

a + b, a − b, a − 3b, ... to 22 terms

Find the sum of the following arithmetic progressions:

a + b, a − b, a − 3b, ... to 22 terms

Find the sum of the following arithmetic progressions

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

Find the sum of the following arithmetic progressions

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

Find the sum of the following arithmetic progressions:

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

Find the sum of the following arithmetic progressions:

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

Find the sum of the following arithmetic progressions:

−26, −24, −22, …. to 36 terms

Find the sum of the following arithmetic progressions:

−26, −24, −22, …. to 36 terms

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

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

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

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

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

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

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?

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?

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

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

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

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

he 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?

he 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?

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.

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.

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?

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?

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

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

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

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

Find the sum of first *n* odd natural numbers

Find the sum of first *n* odd natural numbers

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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.

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

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

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

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

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

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

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

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

Find the sum of first 15 multiples of 8.

Find the sum of first 15 multiples of 8.

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

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

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

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

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

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

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

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

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

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

Find the sum 2 + 4 + 6 ... + 200

Find the sum 2 + 4 + 6 ... + 200

Find the sum 3 + 11 + 19 + ... + 803

Find the sum 3 + 11 + 19 + ... + 803

Find the sums given below :

34 + 32 + 30 + . . . + 10

Find the sums given below :

34 + 32 + 30 + . . . + 10

Find the sum 25 + 28 + 31 + ….. + 100

Find the sum 25 + 28 + 31 + ….. + 100

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

`a_n = 3 + 4n`

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

`a_n = 3 + 4n`

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

b_{n} = 5 + 2n

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

b_{n} = 5 + 2n

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

y_{n} = 9 − 5n

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

y_{n} = 9 − 5n

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

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

Find the sum of the first 25 terms of an A.P. whose *n*th term is given by a_{n} = 2 − 3n.

Find the sum of the first 25 terms of an A.P. whose *n*th term is given by a_{n} = 2 − 3n.

Find the sum of the first 25 terms of an A.P. whose *n*th term is given by a_{n }= 7 − 3n

Find the sum of the first 25 terms of an A.P. whose *n*th term is given by a_{n }= 7 − 3n

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

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

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.

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.

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

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

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

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

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 S_{n}, if a = 5, d = 3 and a_{n} = 50.

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 S_{n}, if a = 5, d = 3 and a_{n} = 50.

Let there be an A.P. with the first term '*a*', common difference'. If *a*_{n} a denotes in *n*^{th} term and *S*_{n} the sum of first *n* terms, find.

n and a, if a_{n} = 4, d = 2 and S_{n}_{ }= −14.

Let there be an A.P. with the first term '*a*', common difference'. If *a*_{n} a denotes in *n*^{th} term and *S*_{n} the sum of first *n* terms, find.

n and a, if a_{n} = 4, d = 2 and S_{n}_{ }= −14.

Let there be an A.P. with the first term 'a', common difference 'd'. If a_{n} a denotes in n^{th} term and S_{n} the sum of first n terms, find.

d, if a = 3, n = 8 and S_{n} = 192.

Let there be an A.P. with the first term 'a', common difference 'd'. If a_{n} a denotes in n^{th} term and S_{n} the sum of first n terms, find.

d, if a = 3, n = 8 and S_{n} = 192.

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 a_{n} = 28, S_{n} = 144 and n= 9.

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 a_{n} = 28, S_{n} = 144 and n= 9.

Let there be an A.P. with the first term '*a*', common difference 'd'. If *a*_{n} a denotes in *n*^{th} term and *S*_{n} the sum of first *n* terms, find.

n and d, if a = 8, a_{n} = 62 and S_{n} = 210

Let there be an A.P. with the first term '*a*', common difference 'd'. If *a*_{n} a denotes in *n*^{th} term and *S*_{n} the sum of first *n* terms, find.

n and d, if a = 8, a_{n} = 62 and S_{n} = 210

Let there be an A.P. with the first term '*a*', common difference '*d*'. If *a*_{n} a denotes in *n*^{th} term and *S*_{n} the sum of first *n* terms, find.

n and a_{n}, if a= 2, d = 8 and S_{n} = 90.

Let there be an A.P. with the first term '*a*', common difference '*d*'. If *a*_{n} a denotes in *n*^{th} term and *S*_{n} the sum of first *n* terms, find.

n and a_{n}, if a= 2, d = 8 and S_{n} = 90.

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?

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.

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.

#### RD Sharma 10 Mathematics

#### Textbook solutions for Class 10th Board Exam

## RD Sharma solutions for Class 10th Board Exam Mathematics chapter 9 - Arithmetic Progression

RD Sharma solutions for Class 10th Board Exam Maths chapter 9 (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.

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Concepts covered in Class 10th Board Exam Mathematics chapter 9 Arithmetic Progression are General Term of an Arithmetic Progression, nth Term of an AP, Sum of First n Terms of an AP, Arithmetic Progression, Derivation of the n th Term, Application in Solving Daily Life Problems, Arithmetic Progressions Examples and Solutions, Terms in a sequence, Geometric Mean, Arithmetic Mean, Sum of the First 'N' Terms of an Geometric Progression, Sum of First n Terms of an AP, General Term of an Geomatric Progression, General Term of an Arithmetic Progression, Geometric Progression, Arithmetic Progression, Introduction to Sequence, Arithmetic Progression Examples and Solutions.

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