The question is given from ncert Book of class 10th Chapter no. 5 Ex. 5.2 Q. 15. In the following question you have to find for what value of n, are the nth terms of two A.P is equal. Give the answer briefly.

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

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Solution:Given two Arithmetic Progressions as; 63, 65, 67,… and 3, 10, 17,….

By taking first Arithmetic Progression,

63, 65, 67, …

a = 63

d = a

_{2}−a_{1}= 65−63 = 2The nth term of this A.P. = a

_{n}= a+(n−1)da= 63+(_{n}n−1)2 = 63+2n−2a= 61+2_{n}n……………………………………….(i)By taking 2nd AP,

3, 10, 17, …

a = 3

d = a

_{2}− a_{1}= 10 − 3 = 7We know that,

nth term of this A.P. = 3+(

n−1)7a= 3+7_{n}n−7a= 7_{n}n−4 ………………………………………………………..(ii)Given, nth term of these A.P.s are equal.

Equating both these eq,

61+2

n= 7n−461+4 = 5

n5

n= 65n= 13i.e The 13th terms of both these Arithmetic Progressions are equal.