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

**Solution:**

The formula for nth term of an AP is an = a + (n - 1) d

Here, an is the nth term, a is the first term, d is the common difference and n is the number of terms.

Let the nth term of the two APs be a_{n }and a_{n}'

Given that the nth term of the two APs is equal.

Since In 1st AP, a = 63 , d = 65 - 3 = 2 and in 2nd AP , a = 3, d = 10 - 3 = 7

Then, 63 + (n - 1)2 = 3 + (n - 1)7......... Equation (1)

By Simplifying Equation (1)

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

7n - 7 - 2n + 2 = 60

5n - 5 = 60

n = 65/5

n = 13

Answer: The 13th term of the two given APs are equal.

**Video Solution:**

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

### NCERT Solutions Class 10 Maths Chapter 5 Exercise 5.2 Question 15 - Chapter 5 Exercise 5.2 Question 15:

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

The value of n for which the nth terms of two APs 63, 65, 67, ... and 3, 10, 17, ... are equal is 13