For what value of n, the nth terms of the arithmetic progressions andare equal?

Given, A.P. = 63, 65, 67,…

A.P.’ = 3, 10, 17,…

Let for A.P.,

First term, a = 63, d = 65 – 63 = 2

And n^th term = a_n

a_n = 63 + (n – 1) 2

= 63 + 2n – 2

= 61 + 2n

For A.P.’

First term, a = 3, d = 10 – 3 = 7

n^th term = a_n

Now n^th term of both A.P. are equal

61 + 2n = -4 + 7n

7n – 2n = 61 + 4

n = 13

Hence, 13^th term of both the A.P. are equal