# 10th CBSE math solution for exercise 5.3

This page 10th CBSE math solution for exercise 5.3 is going to provide you solution for every problems that you find in the exercise no 5.3

## 10th CBSE math solution for exercise 5.3 (1) Find the sum of the following APs

(i)  2 , 7 , 12,....... to 10 terms     Solution

(ii) -37,-33,-29,..................... to 12 terms

(iii) 0.6,1.7,2.8,............... to 100 terms

(iv) 1/15,1/12,1/10,................... to 11 terms

(2) Find the sums given below

(i) 7 + 10 (1/2) + 14 + ...............+ 84

(ii) 34 + 32 + 30 + .................. + 10

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

(3) In an AP

(i) Given a = 5, d = 3, a n= 50 find n and Sn

(ii) Given a = 7, a₁₃ = 35 find d and S₁₃

(iii) Given a₁₂ = 37 , d = 3 find a and S₁₂

(iv) Given a= 15 , S₁₀ = 125 find d and a₁₀

(v) Given d = 5 , S₉ = 75 find a and a

(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 an = 4 , d = 2 ,S n = -14 find n and a

(ix) Given a = 3 , n = 8 ,S n = 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?

(5) The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and common difference.

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

(7) The sum of first 22 terms of an AP in which d = 7and 22nd term is 149.

(8) The sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.

(9) If the sum of 7 terms of an AP is 49 and that of 17 terms is 289,find the sum of first n terms.

(10) Show that a₁,a₂,............ an form an AP where an is defined as below

(i) a n = 3 + 4 n

(ii) a n = 9 - 5 n

Also find the sum of 15 terms in each case.

(11) If the sum of the first n terms of an AP is 4 n - n²  what is the first term (that is S)? what is the sum of first two terms?what is the second term? similarly find the 3rd,the 10th and the nth terms.

(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 odd numbers between 0 and 50.

(15) A contract on construction job specifies a penalty for delay for completion beyond a certain due date as follows. Rs 200 for the first day,Rs 250 for the second day, Rs 300 for the third day etc., the penalty for each succeeding day being Rs 50more than for the preceding day. How much money the contractor has to pay as penalty,if he has delayed the work be 30 days. Solution

(16) A sum of Rs 700 is to be used to seven cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than the preceding prize, find the value of each prizes.Solution

(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 each 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?Solution

(18) A spiral is made up of successive semicircles,with centres alternately at A and B starting with center at A of radii 0.5, 1.0 cm, 1.5 cm ,2.0 cm ......... as shown in figure . What is the total length of spiral made up of thirteen consecutive semicircles. (∏ = 22/7)Solution (19) 200 legs are stacked in the following manner: 20 legs in the bottom row, 19 in the next row,18 in the row next to it and so on. In how many rows are 200 legs placed and how many legs are in the top row. (20) In a potato race, a bucket is placed at the starting point,which is 5 m from the first potato and other potatoes are placed 3 m 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 in the bucket ,runs back to pick up the next potato ,runs to the bucket to drop it in,and she continues in the same way until all the potatoes are in the bucket.What is the total distance the competitor has to run? 