NCERT Solutions for Class 10 Maths Chapter 5

Important NCERT Questions

Arithmetic Progression

NCERT Books for Session 2022-2023

CBSE Board and UP Board Others state Board

EXERCISE 5.2

Page No:106

Questions No:15

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

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First term of first AP = A = 63 and common difference = D = 65 – 63 = 2

Therefore, A_n = A + (n -1)D ⇒ A_n = 63 + (n -1)2

First term of second AP = a = 3 and common difference = d = 10 – 3 = 7

Therefore, a_n = a + (n -1)d ⇒ a_n = 3 +(n -1)7

According to question, A_n = a_n

⇒ 63 + (n – 1)2 = 3 + (n -1)7 ⇒ 63 + 2_n – 2 = 3 + 7_n – 7

⇒ 65 = 5_n ⇒ n = 13

Hence, the 13th term of both the APs are equal.