Q. 154.4( 213 Votes )

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

Answer :

In first AP: a = 63, d = 2


In second AP: a = 3, d = 7


As per question:

nth term of first AP = nth term of second AP

63 + (n – 1) 2 = 3 + (n – 1) 7


63 – 3 + (n – 1) 2 = (n – 1) 7


60 + 2n – 2 = 7n – 7


2n + 58 = 7n – 7


2n + 58 + 7 = 7n


2n + 65 = 7n


7n – 2n = 65


5n =  65


n = 65/5 = 13


Thus, for the 13 value of n, nth term of given two APs will be equal

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