In ncert of class 10th. How i solve the question of arithmetic progressions of exercise 5.2 of math in tricky way. Sir please help me for solving this question. For what value of n, are the nth terms of two APs 63, 65, 67, and 3, 10, 17, … equal?

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# For what value of n, are the nth terms of two APs 63, 65, 67, and 3, 10, 17, … equal? Q.15

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Given two APs as; 63, 65, 67,… and 3, 10, 17,….

Taking first AP,63, 65, 67, …

First term, a = 63

Common difference, d = a

_{2}−a_{1}= 65−63 = 2We know, n

^{th}term of this A.P. = a_{n}= a+(n−1)da= 63+(_{n}n−1)2 = 63+2n−2a= 61+2_{n}n……………………………………….(i)Taking second AP,3, 10, 17, …

First term, a = 3

Common difference, d = a

_{2}− a_{1}= 10 − 3 = 7We know that,

n^{th}term of this A.P. = 3+(n−1)7a= 3+7_{n}n−7a= 7_{n}n−4 ………………………………………………………..(ii)Given,

n^{th}term of these A.P.s are equal to each other.Equating both these equations, we get,

61+2

n= 7n−461+4 = 5

n5

n= 65n= 13Therefore, 13

^{th}terms of both these A.P.s are equal to each other.