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

**Solution:**

The formula for n^{th} term of an AP is aₙ = a + (n - 1) d

Here, aₙ is the n^{th} term, a is the first term, d is the common difference and n is the number of terms.

Let the n^{th} term of the two APs be aₙ_{ }and aₙ'

Given that the n^{th} term of the two APs are equal.

In first AP 63, 65, 67, . . ., a = 63 , d = 65 - 3 = 2

and in second AP 3, 10, 17, . . ., a = 3, d = 10 - 3 = 7

Then,

aₙ = aₙ'

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

The 13^{th} term of the two given APs are equal.

**☛ Check: **NCERT Solutions Class 10 Maths Chapter 5

**Video Solution:**

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

NCERT Solutions Class 10 Maths Chapter 5 Exercise 5.2 Question 15

**Summary:**

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

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