NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions Ex 5.3

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions Ex 5.3 are part of
NCERT Solutions for Class 10 Maths. Here are we have given Chapter 5 Arithmetic Progressions Class 10 NCERT Solutions Ex 5.3. 

BoardCBSE
TextbookNCERT
ClassClass 10
SubjectMaths
ChapterChapter 5
Chapter NameArithmetic Progressions
ExerciseEx 5.3
Number of Questions Solved20
CategoryNCERT Solutions

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions Ex 5.3

Page No: 112

Question 1. Find the sum of the following APs.
(i) 2, 7, 12 ,…., to 10 terms.
(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

Solution :
(i)     2, 7, 12 ,…, to 10 terms
For this AP,
a = 2
d = a2 – a1 = 7 – 2 = 5
n = 10
We know that,
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 28
(ii)     –37, –33, –29 ,…, to 12 terms
For this AP,
a = –37
d = a2 – a1 = (–33) – (–37)
= – 33 + 37 = 4
n = 12
We know that,
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 29
(iii)   0.6, 1.7, 2.8 ,…, to 100 terms
For this AP,
a = 0.6
d = a2 – a1 = 1.7 – 0.6 = 1.1
n = 100
We know that,
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 30
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 31
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 32
Concepts Insight: In order to find the sum of first n terms using Sn = n/2 [2a + (n -1)d] ,first term, common difference and the number of terms is needed. Common difference is the difference in consecutive terms of an AP.

Question 2. Find the sums given below
(i) 7 + 10×1/2 + 14 + ……………… +84
(ii)+ 14 + ………… + 84
(ii) 34 + 32 + 30 + ……….. + 10
(iii) − 5 + (− 8) + (− 11) + ………… + (− 230)

Solution :
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 35

Question 3. In an AP
(i) Given a = 5, d = 3, an = 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 a3 = 15, S10 = 125, find d and a10.
(v) Given d = 5, S9 = 75, find a and a9.
(vi) Given a = 2, d = 8, Sn = 90, find n and an.
(vii) Given a = 8, an = 62, Sn = 210, find n and d.
(viii) Given an = 4, d = 2, Sn = − 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.

Solution :
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 36
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 37
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 38
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 39

Page No: 113

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

Solution :
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 40

Question 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 the common difference.

Solution :
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 41

Question 6. The first and the 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?

Solution :
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 42

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

Solution :
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 43

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

Solution :
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 44

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

Solution :
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 45

Question 10. Show that a1, a2 … , an , … form an AP where an is defined as below
(i) an = 3 + 4n
(ii) an = 9 − 5n
Also find the sum of the first 15 terms in each case.

Solution :
(i)
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 46
(ii)
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 47

Question 11. If the sum of the first n terms of an AP is 4nn2, what is the first term (that is S1)? What is the sum of first two terms? What is the second term? Similarly find the 3rd, the10th and the nth terms.

Solution :
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 48

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

Solution :
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 49

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

Solution :
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 50

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

Solution :
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 51

Question 15. A contract on construction job specifies a penalty for delay of completion beyond a certain dateas 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. 50 more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by 30 days.

Solution :
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 52

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

Solution :
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 53

Question 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?

Solution :
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 54

Question 18. A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre 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 such a spiral made up of thirteen consecutive semicircles? (Take π = 22/7)
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 55

Solution :
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 56

Page No: 114

Question 19. 200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on. In how many rows are the 200 logs placed and how many logs are in the top row?
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 57

Solution :
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 58

Question 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 ten potatoes in the line.
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 59
A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it 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?

Solution :

 

We hope the NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions Ex 5.3 help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions Ex 5.3, drop a comment below and we will get back to you at the earliest.

Leave a Comment