**CBSE NCERT Solutions Chapter 5 Arithmetic Progressions Exercise 5.2 Question 15**

**15. For what value of n, are the nth terms of two AP's : 63, 65, 67 .... and 3, 10, 17, .. equal?**

**Solution:**

Lets first consider AP 63, 65, 67 .....

First term = a = 63

Common difference = d = 65 - 63 = 2

Using formula , to find nth term of arithmetic progression, we can say that

** (1)**

Now, consider second AP 3, 10, 17, ....

First term = a = 3

Common difference = d = 10 -3 = 7

Using formula , to find nth term of arithmetic progression, we can say that

** (2)**

**According to the given condition, we can write**

**(1) = (2)**

**Therefore, 13th terms of both the AP's are equal.**