**Selina Concise Mathematics Class 10 ICSE Solutions Arithmetic Progression**

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**Selina ICSE Solutions for Class 10 Maths Chapter 10 Arithmetic Progression**

**Exercise 10(A)**

**Question 1.**

**Solution:**

**Question 2.**

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

**Solution:**

**Question 3.**

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

**Solution:**

**Question 4.**

Find the 24th term of the sequence:

12, 10, 8, 6,……

**Solution:**

**Question 5.**

**Solution:**

**Question 6.**

**Solution:**

**Question 7.**

**Solution:**

**Question 8.**

Is 402 a term of the sequence :

8, 13, 18, 23,………….?

**Solution:**

**Question 9.**

**Solution:**

**Question 10.**

**Solution:**

**Question 11.**

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

**Solution:**

**Question 12.**

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

**Solution:**

**Question 13.**

**Solution:**

**Question 14.**

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

**Solution:**

**Question 15.**

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

**Solution:**

**Question 16.**

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

**Solution:**

**Question 17.**

Which term of the services :

21, 18, 15, …………. is – 81?

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

**Solution:**

**Exercise 10(B)**

**Question 1.**

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

**Solution:**

**Question 2.**

How many two-digit numbers are divisible by 3?

**Solution:**

**Question 3.**

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

**Solution:**

**Question 4.**

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

**Solution:**

**Question 5.**

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

**Solution:**

**Question 6.**

How many three-digit numbers are divisible by 87?

**Solution:**

**Question 7.**

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?

**Solution:**

**Question 8.**

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

**Solution:**

**Question 9.**

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

**Solution:**

**Question 10.**

**Solution:**

**Question 11.**

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

(i) 4a, 4b and 4c are in A.P

(ii) a + 4, b + 4 and c + 4 are in A.P.

**Solution:**

**Question 12.**

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.

**Solution:**

**Question 13.**

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.

**Solution:**

**Question 14.**

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

**Solution:**

**Question 15.**

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

**Solution:**

**Question 16.**

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

**Solution:**

**Exercise 10(C)**

**Question 1.**

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

**Solution:**

**Question 2.**

How many terms of the A.P. :

24, 21, 18, ……… must be taken so that their sum is 78?

**Solution:**

**Question 3.**

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

**Solution:**

**Question 4(i).**

Find the sum of all odd natural numbers less than 50

**Solution:**

**Question 4(ii).**

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

**Solution:**

**Question 5.**

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

**Solution:**

**Question 6.**

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

**Solution:**

**Question 7.**

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.

**Solution:**

**Question 8.**

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

**Solution:**

**Question 9.**

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?

**Solution:**

**Question 10.**

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.

**Solution:**

**Question 11.**

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.

**Solution:**

**Question 12.**

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

**Solution:**

**Question 13.**

**Solution:**

**Question 14.**

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

**Solution:**

**Exercise 10(D)**

**Solution 1.**

**Solution 2.**

**Solution 3.**

**Solution 4.**

**Solution 5.**

**Solution 6.**

**Solution 7.**

**Solution 8.**

**Solution 9.**

**Solution 10.**

**Solution 11.**

**Solution 12.**

**Solution 13.**

**Solution 14.**

**Exercise 10(E)**

**Solution 1.**

**Solution 2.**

**Solution 3.**

**Solution 4.**

**Solution 5.**

**Solution 6.**

**Solution 7.**

**Exercise 10(F)**

**Solution 1.**

**Solution 2.**

**Solution 3.**

**Solution 4.**

**Solution 5.**

**Solution 6.**

**Exercise 10(G)**

**Solution 1.**

**Solution 2.**

**Solution 3.**

**Solution 4.**

**Solution 5.**

**Solution 6.**

**Solution 7.**

**Solution 8.**

**Solution 9.**

**Solution 10.**

**Solution 11.**

**Solution 12.**

**Solution 13.**

**Solution 14.**

**Solution 15.**

**Solution 16.**

**Solution 17.**

**Solution 18.**

**Solution 19.**

**Solution 20.**

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