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NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions Ex 5.2

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions Ex 5.2 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions Ex 5.2.

  • Arithmetic Progressions Class 10 Ex 5.1
  • Arithmetic Progressions Class 10 Ex 5.2
  • Arithmetic Progressions Class 10 Ex 5.3
  • Arithmetic Progressions Class 10 Ex 5.4
Board CBSE
Textbook NCERT
Class Class 10
Subject Maths
Chapter Chapter 5
Chapter Name Arithmetic Progressions
Exercise Ex 5.2
Number of Questions Solved 20
NCERT Solutions

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions Ex 5.2

Ex 5.2 Class 10 Maths Question 1.
Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the AP:
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 16
Solution:
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 17
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 18

Ex 5.2 Class 10 Maths Question 2.
Choose the correct choice in the following and justify:
(i) 30th term of the AP: 10, 7, 4, …, is
(a) 97
(b) 77
(c) -77
(d) -87

(ii) 11th term of the AP: -3, \(\frac { -1 }{ 2 }\) , 2, …, is
(a) 28
(b) 22
(c) -38
(d) -48
Solution:
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 19

Ex 5.2 Class 10 Maths Question 3.
In the following APs, find the missing terms in the boxes:
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 20
Solution:
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 21
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 22
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 23
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 24
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 25

Ex 5.2 Class 10 Maths Question 4.
Which term of the AP: 3, 8, 13, 18, …, is 78?
Solution:
here, a = 3, d  = 8-3 = 5
Let tn = 78.
Then a = (n-1)d = 78
⇒   3 + (n-1)d x 5 = 78
⇒   n = 16
Thus, 16th term is 78.

Ex 5.2 Class 10 Maths Question 5.
Find the number of terms in each of the following APs:
(i) 7, 13, 19, …, 205
(ii) 18, 15\(\frac { 1 }{ 2 }\), 13, …, -47
Solution:
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 26
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 27

Ex 5.2 Class 10 Maths Question 6.
Check, whether -150 is a term of the AP: 11, 8, 5, 2, ….
Solution:
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 28

Ex 5.2 Class 10 Maths Question 7.
Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.
Solution:
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 29

Ex 5.2 Class 10 Maths Question 8.
An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.
Solution:
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 30

Ex 5.2 Class 10 Maths Question 9.
If the 3rd and the 9th term of an AP are 4 and -8 respectively, which term of this AP is zero?
Solution:
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 31
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 32

Ex 5.2 Class 10 Maths Question 10.
The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
Solution:
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 33

Ex 5.2 Class 10 Maths Question 11.
Which term of the AP: 3, 15, 27, 39, … will be 132 more than its 54th term?
Solution:
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 34

Ex 5.2 Class 10 Maths Question 12.
Two APs have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?
Solution:
Let the first AP be a, a + d, a + 2d, …
and second AP be b, b + d, b + 2d, …
where a ans b are first terms of both APs, and d is the common difference.
Difference of 100th terms = 100        [Given]
⇒    (a + 99d) – (b + 99d) = 100
⇒                    a -b = 100      …(i)
Difference of 1000th terms
= (a + 999d) – (b + 999d)
= a – b           …(ii)
Comparing equations (i) and (ii), we get:
a – b = 100
Hence, the difference of their 1000th terms is 100.

Ex 5.2 Class 10 Maths Question 13.
How many three-digit numbers are divisible by 7?
Solution:
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 35

Ex 5.2 Class 10 Maths Question 14.
How many multiples of 4 lie between 10 and 250?
Solution:
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 36

Ex 5.2 Class 10 Maths Question 15.
For what value of n, the nth term of two APs: 63, 65, 61,… and 3, 10, 17,… are equal?
Solution:
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 37
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 39

Ex 5.2 Class 10 Maths Question 16.
Determine the AP whose 3rd term is 16 and 7th term exceeds the 5th term by 12.
Solution:
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 40

Ex 5.2 Class 10 Maths Question 17.
Find the 20th term from the last term of the AP: 3, 8, 13, …, 253.
Solution:
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 41

Ex 5.2 Class 10 Maths Question 18.
The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
Solution:
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 42
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 43

Ex 5.2 Class 10 Maths Question 19.
Subba Rao started work in 1995 at an annual salary of ₹ 5000 and received an increment of ₹ 200 each year. In which year did his income reach ₹ 7000 ?
Solution:
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 44
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 45

Ex 5.2 Class 10 Maths Question 20.
Ramkali saved ₹ 5 in the first week of a year and then increased her weekly saving by ₹ 1.75. If in the nth week, her weekly saving become ₹ 20.75, find n.
Solution:
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 46
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 47

 

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