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# Selina solutions for Concise Mathematics Class 10 ICSE chapter 10 - Arithmetic Progression [Latest edition]

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## Chapter 10: Arithmetic Progression

Exercise 10(A)Exercise 10(B)Exercise 10(C)Exercise 10(D)Exercise 10(E)Exercise 10(F)

#### Selina solutions for Concise Mathematics Class 10 ICSE Chapter 10 Arithmetic Progression Exercise Exercise 10(A) [Pages 137 - 138]

Exercise 10(A) | Q 1.1 | Page 137

Which of the following are in arithmetic progression

2, 6, 10, 14

Exercise 10(A) | Q 1.2 | Page 137

Which of the following are in arithmetic progression

15, 12, 9, 6

Exercise 10(A) | Q 1.3 | Page 137

Which of the following are in arithmetic progression

5, 9, 12, 18

Exercise 10(A) | Q 1.4 | Page 137

Which of the following are in arithmetic progression

1/2, 1/3 , 1/4 , 1/5

Exercise 10(A) | Q 2 | Page 137

The nth term of the sequence is (2n – 3), find its fifteenth term.

Exercise 10(A) | Q 3 | Page 137

If the pth term of an A.P. is (2p + 3), find the A.P.

Exercise 10(A) | Q 4 | Page 137

Find the 24th term of the sequence: 12, 10, 8, 6,…

Exercise 10(A) | Q 5 | Page 137

Find the 30th term of the sequence

1/2, 1, 3/2,....

Exercise 10(A) | Q 6 | Page 137

Find the 100th term of the sequence:

sqrt3, 2sqrt3, 3sqrt3......

Exercise 10(A) | Q 7 | Page 137

Find the 50th  term of the sequence:

1/n, (n + 1)/n, (2n + 1)/n, ....

Exercise 10(A) | Q 8 | Page 138

Is 402 a term of the sequence:

8, 13, 18, 23.....?

Exercise 10(A) | Q 9 | Page 138

Find the common difference and 99th  term of the arthimetic progression:

7 3/4, 9 1/2, 11 1/4, .....

Exercise 10(A) | Q 10.1 | Page 138

How many terms are there in the series:

4, 7, 10, 13, ........,148?

Exercise 10(A) | Q 10.2 | Page 138

How many terms are there in the series:

0.5, 0.53, 0.56, ......, 1.1?

Exercise 10(A) | Q 10.3 | Page 138

How many terms are there in the series:

3/4, 1, 1 1/4, ......, 3

Exercise 10(A) | Q 11 | Page 138

Which term of the A.P 1 + 4 + 7 + 10 + ..... is  52?

Exercise 10(A) | Q 12 | Page 138

If 5th and 6th terms of an A.P are respectively 6 and 5. Find the 11th term of the A.P

Exercise 10(A) | Q 13 | Page 138

If t_n represents nth term of an A.P t_2 + t_5 - t_3 = 10 and t_2 + t_9 = 17. Find its first term and its common difference.

Exercise 10(A) | Q 14 | Page 138

Find the 10th term from the end of the A.P 4, 9, 14, ..... 254

Exercise 10(A) | Q 15 | Page 138

Determine the arithmetic progression whose 3rd term is 5 and 7th term is 9.

Exercise 10(A) | Q 16 | Page 138

Find the 31st term of an A.P whose 10th term is 38 and the 10th term is 74

Exercise 10(A) | Q 17 | Page 138

Which term of the service

21, 18, 15 ...... is -81?

Can any term of this series be zero? if yes find the number of terms.

Exercise 10(A) | Q 18 | Page 138

An A.P. consists of 60 terms, If the first and the last terms be 7 and 125 respectively, find the 31st term.

Exercise 10(A) | Q 19 | Page 138

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

Exercise 10(A) | Q 20 | Page 138

If the third term of an A.P. is 5 and the seventh term is 9, find the 17th term.

#### Selina solutions for Concise Mathematics Class 10 ICSE Chapter 10 Arithmetic Progression Exercise Exercise 10(B) [Page 140]

Exercise 10(B) | Q 1 | Page 140

In an A.P., ten times of its tenth term is equal to thirty times of its 30th term. Find its 40th term.

Exercise 10(B) | Q 2 | Page 140

How many two-digit numbers are divisible by 3?

Exercise 10(B) | Q 3 | Page 140

Which term of A.P. 5, 15, 25 ………… will be 130 more than its 31st term?

Exercise 10(B) | Q 4 | Page 140

Find the value of p, if x, 2x + p and 3x + 6 are in A.P

Exercise 10(B) | Q 5 | Page 140

If the 3rd and the 9th terms of an arithmetic progression are 4 and -8 respectively, Which term of it is zero?

Exercise 10(B) | Q 6 | Page 140

How many three-digit numbers are divisible by 87?

Exercise 10(B) | Q 7 | Page 140

For what value of n, the nth term of A.P 63, 65, 67, …….. and nth term of A.P. 3, 10, 17,…….. are equal to each other?

Exercise 10(B) | Q 8 | Page 140

Determine the A.P. Whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.

Exercise 10(B) | Q 9 | Page 140

If number n - 2, 4n - 1 and 5n + 2 are in A.P find the value of n and its next two terms.

Exercise 10(B) | Q 10 | Page 140

Determine the value of k for which k^2 + 4k + 8, 2k^2 + 3k + 6 and 3k^2 + 4k + 4 are in A.P.

Exercise 10(B) | Q 11.1 | Page 140

If a, b and c are in A.P show that 4a, 4b and 4c are in A.P

Exercise 10(B) | Q 11.2 | Page 140

If a, b and c are in A.P show that: a + 4, b + 4 and c + 4 are in A.P.

Exercise 10(B) | Q 12 | Page 140

An A.P consists of 57 terms of which 7th term is 13 and the last term is 108. Find the 45th term of this A.P.

Exercise 10(B) | Q 13 | Page 140

4th term of an A.P is equal to 3 times its first term and 7th term exceeds twice the 3rd time by I. Find the first term and the common difference.

Exercise 10(B) | Q 14 | Page 140

The sum of the 2nd term and the 7th term of an A.P is 30. If its 15th term is 1 less than twice of its 8th term, find the A.P

Exercise 10(B) | Q 15 | Page 140

In an A.P, if mth term is n and nth term is m, show that its rth term is (m + n – r)

Exercise 10(B) | Q 16 | Page 140

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

#### Selina solutions for Concise Mathematics Class 10 ICSE Chapter 10 Arithmetic Progression Exercise Exercise 10(C) [Pages 143 - 144]

Exercise 10(C) | Q 1 | Page 143

Find the sum of the first 22 terms of the A.P.: 8, 3, -2, ………

Exercise 10(C) | Q 2 | Page 143

How many terms of the A.P: 24, 21, 18, ……… must be taken so that their sum is 78?

Exercise 10(C) | Q 3 | Page 143

Find the sum of 28 terms of an A.P. whose nth term is 8n - 5.

Exercise 10(C) | Q 4.1 | Page 143

Find the sum of all odd natural numbers less than 50

Exercise 10(C) | Q 4.2 | Page 143

Find the sum of first 12 natural numbers each of which is a multiple of 7.

Exercise 10(C) | Q 5 | Page 143

Find the sum of first 51 terms of an A.P. whose 2nd and 3rd terms are 14 and 18 respectively.

Exercise 10(C) | Q 6 | Page 143

The sum of the first 7 terms of an A.P is 49 and that of the first 17 terms of it is 289. Find the sum of first n terms

Exercise 10(C) | Q 7 | Page 143

The first term of an A.P is 5, the last term is 45 and the sum of its terms is 1000. Find the number of terms and the common difference of the A.P.

Exercise 10(C) | Q 8 | Page 143

Find the sum of all natural numbers between 250 and 1000 which are divisible by 9.

Exercise 10(C) | Q 9 | Page 143

The first and the last terms of an A.P. are 34 and 700 respectively. If the common difference is 18, how many terms are there and what is their sum?

Exercise 10(C) | Q 10 | Page 144

In an A.P, the first term is 25, nth term is -17 and the sum of n terms is 132. Find n and the common difference.

Exercise 10(C) | Q 11 | Page 144

If the 8th term of an A.P is 37 and the 15th term is 15 more than the 12th term, find the A.P. Also, find the sum of first 20 terms of A.P.

Exercise 10(C) | Q 12 | Page 144

Find the sum of all multiples of 7 between 300 and 700.

Exercise 10(C) | Q 13 | Page 144

The sum of n natural number is 5n^2 + 4n. Find its 8th term.

Exercise 10(C) | Q 14 | Page 144

The fourth term of an A.P. is 11 and the term exceeds twice the fourth term by 5 the A.P and the sum of first 50 terms

#### Selina solutions for Concise Mathematics Class 10 ICSE Chapter 10 Arithmetic Progression Exercise Exercise 10(D) [Page 146]

Exercise 10(D) | Q 1 | Page 146

Find three numbers in A.P whose sum is 24 and whoseproduct is 440

Exercise 10(D) | Q 2 | Page 146

The sum of three consecutive terms of an A.P. is 21 and the sum of their squares is 165. find these terms.

Exercise 10(D) | Q 3 | Page 146

The angle of a quadrillateral are A.P. with common difference 20°.find its angles.

Exercise 10(D) | Q 4 | Page 146

Divide 96 into four parts which are in A.P and the ratio between product of their means to product of their extremes is 15:7.

Exercise 10(D) | Q 5 | Page 146

Find five numbers in A.P whose sum is 12 1/2 and the ratio of the first to the last terms 2:3.

Exercise 10(D) | Q 6 | Page 146

Split 207 into three parts such that these partsare in A.P. and the productof the two smaller parts in 4623.

Exercise 10(D) | Q 7 | Page 146

The sum of three numbers in A.P.is 15 the sum of the square of the exterme is 58. find the numbers.

Exercise 10(D) | Q 8 | Page 146

Find four numbers in A.P. whose sum is 20 and the sum of whose squares is 120.

Exercise 10(D) | Q 9 | Page 146

Insert one arithmetic mean between 3 and 13.

Exercise 10(D) | Q 10 | Page 146

The angles of a polygon are in A.P. with common differance 5°. if the smallest angle in 120°, find the number ofsides of the polygoa.

Exercise 10(D) | Q 11 | Page 146

1/a,1/b and 1/c are in A.P show that : bc,ca and ab also in A.P.

#### Selina solutions for Concise Mathematics Class 10 ICSE Chapter 10 Arithmetic Progression Exercise Exercise 10(E) [Page 147]

Exercise 10(E) | Q 1 | Page 147

Two cars start together in the same direction from the same place. The first cargoes at uniform speed of 10 km h-1. The second car goes at a speed of 8 km h-1 in the first hour and thereafter increasing the speed by 0.5 km h-1 each succeeding hour. After how many hours will the two cars meet?

Exercise 10(E) | Q 2 | Page 147

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

Exercise 10(E) | Q 3 | Page 147

An article can be bought by paying Rs. 28,000 at once or by making 12 monthly installments. If the first installment paid is Rs. 3,000 and every other installments is Rs. 100 less than the previous one, find :

(i) amount of installments paid in the 9th month

(ii) total amount paid in the installment scheme

Exercise 10(E) | Q 4 | Page 147

A manufacturer of TV sets produces 600 units in the third year and 700 units in the 7th year. Assuming that the production increases uniformly by a fixed number every year find:

(i) the production in the first year.

(ii) the production in the 10th year.

(iii) the total production in 7 years.

Exercise 10(E) | Q 5 | Page 147

Mrs. Gupta repays her total loan of Rs. 1,18,000 by paying installments every month. If the installments for the first month is Rs. 1,000 and it increases by Rs. 100 every month, What amount will she pays as the 30th installments of loan? What amount of loan she still has to pay after the 30th installments

#### Selina solutions for Concise Mathematics Class 10 ICSE Chapter 10 Arithmetic Progression Exercise Exercise 10(F) [Page 148]

Exercise 10(F) | Q 1 | Page 148

The 6th term of an A.P. is 16 and the 14th term is 32. Determine the 36th term.

Exercise 10(F) | Q 2 | Page 148

If the third and the 9th term of an A.P. be 4 and -8 respectively, find which term is zero?

Exercise 10(F) | Q 3 | Page 148

An A.P. consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term of the A.P.

Exercise 10(F) | Q 4.1 | Page 148

Find the arithmetic mean of:
-5 and 41

Exercise 10(F) | Q 4.2 | Page 148

Find the arithmetic mean of:
3x - 2y and 3x + 2y

Exercise 10(F) | Q 4.3 | Page 148

Find the arithmetic mean of:
(m + n)and (m - n)2

Exercise 10(F) | Q 5 | Page 148

Find the sum of first 10 terms of the A.P.

4 + 6 + 8 + ……

Exercise 10(F) | Q 6 | Page 148

Find the sum of first 20 terms of an A.P. whose first term is 3 and the last term is 57.

Exercise 10(F) | Q 7 | Page 148

How many terms of the series 18 + 15 + 12 + …….. when added together will give 45?

Exercise 10(F) | Q 8 | Page 148

The nth term of a sequence is 8 - 5n. Show that the sequence is an A.P.

Exercise 10(F) | Q 9 | Page 148

Find the general term (nth term) and 23rd term of the sequence 3, 1, -1, -3, ….. .

Exercise 10(F) | Q 10 | Page 148

Which term of the sequence 3, 8, 13, ........ is 78?

Exercise 10(F) | Q 11 | Page 148

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

Exercise 10(F) | Q 12 | Page 148

How many two digit numbers are divisible by 3?

Exercise 10(F) | Q 13 | Page 148

How many multiples of 4 lie between 10 and 250?

Exercise 10(F) | Q 14 | Page 148

The sum of the 4th and the 8th terms of an A.P. is 24 and the sum of the sixth term and the tenth is 44. Find the first three terms of the A.P.

Exercise 10(F) | Q 15 | Page 148

The sum of first 14 terms of an A.P. is 1050 and its 14th term is 140. Find the 20th term.

Exercise 10(F) | Q 16 | Page 148

The 25th term of an A.P. exceeds its 9th term by 16. Find its common difference.

Exercise 10(F) | Q 17 | Page 148

For an A.P., show that:

(m + n)th term + (m - n)th term = 2 × mthterm

Exercise 10(F) | Q 18 | Page 148

If the nth term of the A.P. 58, 60, 62,.... is equal to the nth term of the A.P. -2, 5, 12, …., find the value of n.

Exercise 10(F) | Q 19 | Page 148

Which term of the A.P. 105, 101, 97 … is the first negative term?

Exercise 10(F) | Q 20 | Page 148

How many three digit numbers are divisible by 7?

Exercise 10(F) | Q 21 | Page 148

Divide 216 into three parts which are in A.P. and the product of the two smaller parts is 5040.

Exercise 10(F) | Q 22 | Page 148

Can 2n2 - 7 be the nth term of an A.P? Explain.

Exercise 10(F) | Q 23 | Page 148

Find the sum of the A.P., 14, 21, 28, …, 168.

Exercise 10(F) | Q 24 | Page 148

The first term of an A.P. is 20 and the sum of its first seven terms is 2100; find the 31st term of this A.P.

Exercise 10(F) | Q 25 | Page 148

Find the sum of last 8 terms of the A.P. -12, -10, -8, ……, 58.

## Chapter 10: Arithmetic Progression

Exercise 10(A)Exercise 10(B)Exercise 10(C)Exercise 10(D)Exercise 10(E)Exercise 10(F)

## Selina solutions for Concise Mathematics Class 10 ICSE chapter 10 - Arithmetic Progression

Selina solutions for Concise Mathematics Class 10 ICSE chapter 10 (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 CISCE Concise Mathematics Class 10 ICSE solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Concise Mathematics Class 10 ICSE chapter 10 Arithmetic Progression are Arithmetic Progression - Finding Their General Term, Arithmetic Progression - Finding Sum of Their First ‘N’ Terms., Simple Applications of Arithmetic Progression.

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