#### Class 10

#### 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?