## Ncert Solutions for Class 10

#### Arithmetic Progressions

#### Arithmetic Progressions

#### Exercise 5.1

(iv) *a *= – 1, \(d=\frac{1}{2}\)

3. For the following APs, write the first term and the common difference:

(iii) \(\frac{1}{3}, \frac{5}{3}, \frac{9}{3}, \frac{13}{3}, …\)

(ii) \(2, \frac{5}{2}, 3, \frac{7}{2}, …\)

(iii) -1.2, -3.2, -5.2, -7.2, …

(v) 3, \(3+\sqrt2\), \(3+2\sqrt2\), \(3+3\sqrt2\), …

(vi) 0.2, 0.22, 0.222, 0.2222, …

(viii) \(-\frac{1}{2}, -\frac{1}{2}, -\frac{1}{2}, …\)

(xii) \(\sqrt2, \sqrt8,\)\(\sqrt{18}, \sqrt{32}, …\)

(xiii) \(\sqrt3, \sqrt6, \sqrt9, \sqrt{12}, …\)

#### Arithmetic Progressions

#### Exercise 5.2

1. Fill in the blanks in the following table, given that *a *is the first term, *d *the common difference and \(*a_**n\) *the *n*th term of the AP:

2. Choose the correct choice in the following and justify:

(i) 30th term of the AP: 10, 7, 4, . . . , is

(ii) 11^{th} term of the A.P.: \(-3, -\frac{1}{2}, 2, …\) is:

3. In the following APs, find the missing terms in the boxes:

4. Which term of the AP : 3, 8, 13, 18, . . . ,is 78?

5. Find the number of terms in each of the following APs:

(ii) 18, \(15\frac{1}{2}\), 13, …, -47

6. Check whether – 150 is a term of the AP: 11, 8, 5, 2 . . .

7. Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.

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

9. If the 3rd and the 9th terms of an AP are 4 and – 8 respectively, which term of this AP is zero?

10. The 17th term of an AP exceeds its 10th term by 7. Find the common difference.

11. Which term of the AP: 3, 15, 27, 39, . . . will be 132 more than its 54th term?

13. How many three-digit numbers are divisible by 7?

14. How many multiples of 4 lie between 10 and 250?

15. For what value of *n*, are the *n*th terms of two APs: 63, 65, 67, . . . and 3, 10, 17, . . . equal?

16. Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.

17. Find the 20th term from the last term of the AP: 3, 8, 13, . . ., 253.

#### Arithmetic Progressions

#### Exercise 5.3

1. Find the sum of the following APs:

(ii) – 37, – 33, – 29 ,…, to 12 terms

(iii) 0.6, 1.7, 2.8 ,……, to 100 terms

(iv) \({1 \over 15}, {1 \over 12}, {1 \over 10}, … \) to 11 terms.

(i) \(7 + 10 {1 \over 2} + 14 + ………… + 84 \)

(iii) -5 + ( -8) + ( -11) + ………… + ( -230)

(i) Given a = 5, d = 3, \(a_n = 50 \), find n and \(S_n \).

(ii) Given a = 7, \(a_{13} = 35 \), find d and \(S_{13} \).

(iii) Given \(a_{12} = 37 \), d = 3, find a and \(S_{12} \).

(iv) Given \(a_3 = 15 \), \(S_{10} = 125 \), find d and \(a_{10} \).

(v) Given d = 5, \(S_9 = 75 \), find a and \(a_9 \).

(vi) Given a = 2, d = 8, \(S_n = 90 \), find n and \(a_n \).

(vii) Given a = 8, \(a_n = 62 \), \(S_n = 210 \), find n and d.

(viii) Given \(a_n = 4 \), d = 2, \(S_n = -14 \), find n and a.

(ix) Given a = 3, n = 8, S = 192, find d.

(x) Given l = 28, S = 144 and there are total 9 terms. Find a.

4. How many terms of the AP. 9, 17, 25 … must be taken to give a sum of 636?

7. Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.

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

10. Show that \(a_1, a_2 … , a_n , … \) form an AP where an is defined as below:

Also find the sum of the first 15 terms in each case.

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

13. Find the sum of first 15 multiples of 8.

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

17. In a school, students thought of planting 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 the same as the class, in

which they are studying, e.g., a section of class I will plant 1 tree, a section of class II will plant 2 trees and so on till class XII. There are three sections of each class. How many trees will be planted by the students?