#### Chapters

Chapter 2: Polynomials

Chapter 3: Linear Equations in two variables

Chapter 4: Triangles

Chapter 5: Trigonometric Ratios

Chapter 6: T-Ratios of some particular angles

Chapter 7: Trigonometric Ratios of Complementary Angles

Chapter 8: Trigonometric Identities

Chapter 9: Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive

Chapter 10: Quadratic Equations

Chapter 11: Arithmetic Progression

Chapter 12: Circles

Chapter 13: Constructions

Chapter 14: Height and Distance

Chapter 15: Probability

Chapter 16: Coordinate Geomentry

Chapter 17: Perimeter and Areas of Plane Figures

Chapter 18: Area of Circle, Sector and Segment

Chapter 19: Volume and Surface Area of Solids

#### R.S. Aggarwal Secondary School Mathematics Class 10 (for 2019 Examination)

## Chapter 11: Arithmetic Progression

#### Chapter 11: Arithmetic Progression solutions [Page 0]

Show that each of the progressions given below is an AP. Find the first term, common difference and next term of each.

(i) 9, 15, 21, 27,…………

Show that each of the progressions given below is an AP. Find the first term, common difference and next term of each

(ii) 11, 6, 1, – 4,……..

Show that each of the progressions given below is an AP. Find the first term, common difference and next term of each .

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

Show that each of the progressions given below is an AP. Find the first term, common difference and next term of each.

(iv) 2, 8, 18, 32,..........

Show that each of the progressions given below is an AP. Find the first term, common difference and next term of each.

(v) `sqrt(20)`, `sqrt(45)`, `sqrt(80)`, `sqrt(125)`,.........

Find:

(i) the 20^{th } term of the AP 9,13,17,21,..........

Find:

(ii) the 35^{th} term of AP 20,17,14,11,..........

Find:

the 18^{th } term of the AP `sqrt(2), sqrt (18), sqrt(50), sqrt(98)`,...........

Find:

the 9^{th } term of the AP `3/4 , 5/4 , 7/4 , 9/4 ,.........`

Find:

v) the 15the term of the AP - 40,- 15,10,35,.........

Find the 37^{th } term of the AP 6 , 7 `3/4 , 9 1/2 , 11 1/4,.............`

Find the 25^{th} term of the AP 5 , 4`1/2 , 4,3 1/2 ,3`.................

Find the nth term of the following Aps:

(i) 5, 11, 17, 23 …

Find the nth term of the following Aps:

16, 9, 2, -5, …..

If the nth term of a progression is (4n – 10) show that it is an AP. Find its

(i) first term, (ii) common difference (iii) 16 the term.

How many terms are there in the AP 6,1 0, 14, 18, ….., 174?

How many terms are there in the AP 41, 38, 35, ….,8?

How many terms are there in the AP 18,15 `1/2 `, 13 , ........... -47.?

Which term of term of the AP 3,8,13,18,….. is 88?

Which term of AP 72,68,64,60,… is 0?

Which term of the AP ` 5/6 , 1 , 1 1/6 , 1 1/3` , ................ is 3 ?

Which term of the AP 21, 18, 15, …… is -81?

Which term of the AP 3,8, 13,18,…. Will be 55 more than its 20^{th} term?

Which term of the AP 5, 15, 25, ….. will be 130 more than its 31^{st} term?

If the 10^{th } term of an AP is 52 and 1^{7th} term is 20 more than its 13^{th } term, find the AP

Find the middle term of the AP 6, 13, 20, …., 216.

Find the middle term of the AP 10, 7, 4, ……., (-62).

Find the sum of two middle most terms of the AP `- 4/3 , -1 (-2)/3, ....., 4 1/3.`

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

Find the 6^{th } term form the end of the AP 17, 14, 11, ……, (-40).

Is 184 a term of the AP 3, 7, 11, 15, ….?

Is -150 a term of the AP 11, 8, 5, 2, ……?

Which term of the AP 121, 117, 113, …. is its first negative term?

Which term of the AP `20, 19 1/4 , 18 1/2 , 17 3/4 ` ,..... is the first negative term?

The 7^{th} term of the an AP is -4 and its 13^{th} term is -16. Find the AP.

The 4^{th} term of an AP is zero. Prove that its 25^{th} term is triple its 11^{th} term.

The 8^{th} term of an AP is zero. Prove that its 38^{th} term is triple its 18^{th} term.

The 4^{th} term of an AP is 11. The sum of the 5^{th} and 7^{th} terms of this AP is 34. Find its common difference

The 9^{th} term of an AP is -32 and the sum of its 11^{th} and 13^{th} terms is -94. Find the common difference of the AP.

Determine the nth term of the AP whose 7^{th} term is -1 and 16^{th} term is 17.

If 4 times the 4^{th} term of an AP is equal to 18 times its 18^{th} term then find its 22^{nd} term.

If 10 times the 10^{th } term of an AP is equal to 15 times the 15^{th} term, show that its 25^{th} term is zero.

Find the common difference of an AP whose first term is 5 and the sum of its first four terms is half the sum of the next four terms.

The sum of the 2^{nd} and 7^{th} terms of an AP is 30. If its 15^{th} term is 1 less than twice its 8^{th} term, find AP.

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

The 17^{th} term of AP is 5 more than twice its 8^{th} term. If the 11^{th} term of the AP is 43, find its nth term.

The 24^{th} term of an AP is twice its 10^{th} term. Show that its 72^{nd} term is 4 times its 15^{th} term.

The 19^{th} term of an AP is equal to 3 times its 6^{th} term. If its 9^{th} term is 19, find the AP.

If the pth term of an AP is q and its qth term is p then show that its (p + q)th term is zero

The first and last terms of an AP are a and l respectively. Show that the sum of the nth term from the beginning and the nth term form the end is ( a + l ).

How many two-digit number are divisible by 6?

How many two-digits numbers are divisible by 3?

How many three-digit numbers are divisible by 9?

How many numbers are there between 101 and 999, which are divisible by both 2 and 5?

In a flower bed, there are 43 rose plants in the first row, 41 in second, 39 in the third, and so on. There are 11 rose plants in the last row. How many rows are there in the flower bed?

A sum of ₹2800 is to be used to award four prizes. If each prize after the first is ₹200 less than the preceding prize, find the value of each of the prizes

#### Chapter 11: Arithmetic Progression solutions [Page 0]

Determine k so that (3k -2), (4k – 6) and (k +2) are three consecutive terms of an AP.

Find the value of x for which the numbers (5x + 2), (4x - 1) and (x + 2) are in AP.

If (3y – 1), (3y + 5) and (5y + 1) are three consecutive terms of an AP then find the value of y.

Find the value of x for which (x + 2), 2x, ()2x + 3) are three consecutive terms of an AP.

Show that `(a-b)^2 , (a^2 + b^2 ) and ( a^2+ b^2) ` are in AP.

Find the three numbers in AP whose sum is 15 and product is 80.

The sum of three numbers in AP is 3 and their product is -35. Find the numbers.

Divide 24 in three parts such that they are in AP and their product is 440.

The sum of three consecutive terms of an AP is 21 and the sum of the squares of these terms is 165. Find these terms

The angles of quadrilateral are in whose AP common difference is 10° . Find the angles.

Find four numbers in AP whose sum is 8 and the sum of whose squares is 216.

Divide 32 into four parts which are the four terms of an AP such that the product of the first and fourth terms is to product of the second and the third terms as 7:15.

The sum of first three terms of an AP is 48. If the product of first and second terms exceeds 4 times the third term by 12. Find the AP.

#### Chapter 11: Arithmetic Progression solutions [Page 0]

The first three terms of an AP are respectively (3y – 1), (3y + 5) and (5y + 1), find the value of y .

If k,(2k - 1) and (2k - 1) are the three successive terms of an AP, find the value of k.

If 18, a, (b - 3) are in AP, then find the value of (2a – b)

If the numbers a, 9, b, 25 from an AP, find a and b.

If the numbers (2n – 1), (3n+2) and (6n -1) are in AP, find the value of n and the numbers

How many three-digit natural numbers are divisible by 7?

How many three-digit natural numbers are divisible by 9?

If the sum of first m terms of an AP is ( 2m^{2} + 3m) then what is its second term?

What is the sum of first n terms of the AP a, 3a, 5a, …..

What is the 5^{th } term form the end of the AP 2, 7, 12, …., 47?

If a_{n } denotes the nth term of the AP 2, 7, 12, 17, … find the value of (a_{30 }- a_{20} ).

The nth term of an AP is (3n +5 ). Find its common difference.

The nth term of an AP is (7 – 4n). Find its common difference.

Write the next term for the AP` sqrt( 8), sqrt(18), sqrt(32),.........`

Write the next term of the AP `sqrt(2) , sqrt(8) , sqrt(18),.........`

Which term of the AP 21, 18, 15, … is zero?

Find the sum of the first n natural numbers.

Find the sum of first n even natural numbers.

The first term of an AP is p and its common difference is q. Find its 10^{th} term.

If ` 4/5 ` , a , 2 are in AP, find the value of a.

If (2p +1), 13, (5p -3) are in AP, find the value of p.

If (2p – 1), 7, 3p are in AP, find the value of p.

If the sum of first p terms of an AP is 2 (ap^{2} + bp), find its common difference.

If the sum of first n terms is (3n^{2 }+ 5n), find its common difference.

Find an AP whose 4^{th } term is 9 and the sum of its 6^{th} and 13^{th} terms is 40.

#### Chapter 11: Arithmetic Progression solutions [Page 0]

Find the sum of the following Aps:

i) 2, 7, 12, 17, ……. to 19 terms .

Find the sum of the following Aps:

9, 7, 5, 3 … to 14 terms

Find the sum of the following Aps:

-37, -33, -29, … to 12 terms.

Find the sum of the following Aps:

`1/15 , 1/12 , 1/10 `, ................. to 11 terms.

`Find the sum of the following Aps:`

`0.6, 1.7, 2.8, …. to 100 terms`

Find the sum of the following arithmetic series:

`7 + 10 1/2 + 14 + ....... + 84`

Find the sum of the following arithmetic series:

34 + 32 + 30 +...+10

Find the sum of the following arithmetic series:

(-5)+(-8)+(-11)+...+(-230)

Find the sum of first n terms of an AP whose nth term is (5 - 6n). Hence, find the sum of its first 20 terms.

The sum of the first n terms of an AP is (3n^{2}+6n) . Find the nth term and the 15^{th} term of this AP.

The sum of the first n terms of an AP is given by `s_n = ( 3n^2 - n) ` Find its

(i) nth term,

(ii) first term and

(iii) common difference.

The sum of the first n terms of an AP in `((5n^2)/2 + (3n)/2)`.Find its nth term and the 20th term of this AP.

The sum of the first n term sofa an AP is `( (3n^2) /2 +(5n) /2)`. Find its nth term and the 25th term

How many terms of the AP 21, 18, 15, … must be added to get the sum 0?

How many terms of the AP 9, 17, 25, … must be taken so that their sum is 636?

How many terms of the AP 63, 60, 57, 54, ….. must be taken so that their sum is 693? Explain the double answer.

How many terms of the AP ` 20, 19 1/3 , 18 2/3` , .........must be taken so that their sum is 300? Explain the double answer.

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

Find the sum of all natural numbers between 200 and 400 which are divisible by 7.

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

Find the sum of first 15 multiples of 8.

Find the sum of all multiples of 9 lying between 300 and 700.

Find the sum of all three-digits natural numbers which are divisible by 13.

Find the sum of first 100 even number which are divisible by 5.

Find the sum of the following.

`(1 - 1/n) +(1 -2/n) + (1- 3/n) +` ......up to n terms.

In an AP. It is given that `s_5 + s_7 = 167 and s_10 = 235 ," then find the AP, where " S_n` denotes the sum of its first n terms.

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.

In an AP, the first term is -4, the last term is 29 and the sum of all its terms is 150. Find its common difference.

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

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

In an AP, the first term is 22, nth terms is -11 and sum of first n terms is 66. Find the n and hence find the4 common difference.

The 12^{th} term of an AP is -13 and the sum of its first four terms is 24. Find the sum of its first 10 terms.

The sum of the first 7 terms of an AP is 182. If its 4^{th} and 17^{th } terms are in the ratio 1:5, find the AP.

The sum of the first 9 terms of an AP is 81 and that of its first 20 terms is 400. Find the first term and common difference of the AP.

The sum of the first 7 terms of an AP is 49 and the sum of its first 17 term is 289. Find the sum of its first n terms.

Two Aps have the same common difference. If the fist terms of these Aps be 3 and 8 respectively. Find the difference between the sums of their first 50 terms.

The sum first 10 terms of an AP is -150 and the sum of its next 10 terms is -550 . Find the AP.

The 13^{th} terms of an AP is 4 times its 3^{rd} term. If its 5^{th} term is 16, Find the sum of its first 10 terms.

The 16^{th} term of an AP is 5 times its 3^{rd} term. If its 10^{th} term is 41, find the sum of its first 15 terms.

An AP 5, 12, 19, .... has 50 term. Find its last term. Hence, find the sum of its last 15 terms.

An AP 8, 10, 12, … has 60 terms. Find its last term. Hence, find the sum of its last 10 terms.

The sum of the 4^{th} and 8^{th} terms of an AP is 24 and the sum of its 6^{th} and 10^{th} terms is 44. Find the sum of its first 10 terms.

The sum of fist m terms of an AP is ( 4m^{2} - m). If its nth term is 107, find the value of n. Also, Find the 21^{st} term of this AP.

The sum of first q terms of an AP is (63q - 3q^{2)} . If its pth term is -60, find the value of p. Also, find the 11^{th} term of its AP.

Find the number of terms of the AP -12, -9, -6, .., 21. If 1 is added to each term of this AP then the sum of all terms of the AP thus obtained.

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

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

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 section, find how many trees were planted by student. Which value is shown in the question?

In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato, and the other potatoes are placed 3m apart in a straight line. There are 10 potatoes in the line. A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and he continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?

There are 25 trees at equal distance of 5 m in a line with a water tank, the distance of the

water tank from the nearest tree being 10 m. A gardener waters all the trees separately,

starting from the water tank and returning back to the water tank after watering each tree to get water for the next. Find the total distance covered by the gardener in order to water all the trees.

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

A man saved ₹33000 in 10 months. In each month after the first, he saved ₹100 more than he did in the preceding month. How much did he save in the first month?

A man arranges to pay off debt of ₹36000 by 40 monthly instalments which form an arithmetic series. When 30 of the installments are paid, he dies leaving on-third of the debt

unpaid. Find the value of the first instalment.

A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: ₹200 for the first day, ₹ 250 for the second day, ₹300 for the third day, etc. the penalty for each succeeding day being ₹50 more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by 30 days?

## Chapter 11: Arithmetic Progression

#### R.S. Aggarwal Secondary School Mathematics Class 10 (for 2019 Examination)

#### Textbook solutions for Class 10

## R.S. Aggarwal solutions for Class 10 Mathematics chapter 11 - Arithmetic Progression

R.S. Aggarwal solutions for Class 10 Maths chapter 11 (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 Secondary School Mathematics for Class 10 (for 2019 Examination) solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 10 Mathematics chapter 11 Arithmetic Progression are 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.

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