For what value of n are the nth term of two aps 60, 62, 64

For what value of n, are the nth terms of two APs 63, 65, 67, and 3, 10, 17, … equal? Maths Q&A

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Last updated at March 19, 2021 by

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Last updated at March 19, 2021 by Teachoo

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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 aₙ and aₙ'

Given that the nth 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 13th term of the two given APs are equal.

☛ Check: NCERT Solutions Class 10 Maths Chapter 5

Video Solution:

NCERT Solutions Class 10 Maths Chapter 5 Exercise 5.2 Question 15

Summary:

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

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