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

Question

Philoid · Accepted Answer

We have to find the value of n, so that the nth term in the both series should be equal

63, 65, 67, ….

In the above series

First term (a₁) = 63,

Common difference (d₁) = 2

3, 10, 17, ….

First term (a₂) = 3,

Common difference (d₂) = 7

Since value of n^th term is equal we equate a_n of both the series.

a_n1 = a_n2

a₁ + (n-1)d₁ = a₂ + (n-1)d₂

63 + (n-1)2 = 3 + (n-1)7

61 +2n = 7n – 4

5n = 65

n = 13.