**Solution:**

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

Consider the first AP,

63, 65, 67, …

First term, a = 63

Common difference, d = a_{2 }− a_{1} = 65−63 = 2

We know that, the n^{th} term of this AP = a_{n} = a + (n − 1)d

a_{n} = 63 + (n − 1)2 = 63 + 2n − 2

a_{n} = 61 + 2n ………………………………………. **(i)**

Consider the second AP,

3, 10, 17, …

First term, a = 3

Common difference, d = a_{2} − a_{1} = 10 − 3 = 7

We know that,

n ^{th} term of this AP = 3 + (n − 1)7

a_{n} = 3 + 7n − 7

a_{n} = 7n − 4 ……………………………………………………….. **(ii)**

Given, that the n^{th} terms of these APs are equal to each other.

Equating both equations, we get;

61 + 2n = 7n − 4

61 + 4 = 5n

5n = 65

n = 13

Therefore, the 13^{th} terms of both these APs are equal to each other.