NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 15

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 15

Question:

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

Given:

Two Arithmetic Progressions (APs):

AP1: 63, 65, 67, ...

AP2: 3, 10, 17, ...

To Find:

The value of n for which the nth terms of AP1 and AP2 are equal.

Formula:

The nth term of an AP is given by an = a + (n-1)d, where 

'a' is the first term and 

'd' is the common difference.

Solution:

For AP1: 

a = 63, 

d = 65 - 63 = 2

⇒ an = 63 + (n-1)2 

⇒ an = 63 + 2n - 2 

⇒ an = 61 + 2n

For AP2: 

a = 3, 

d = 10 - 3 = 7

⇒ an = 3 + (n-1)7 

⇒ an = 3 + 7n - 7

⇒ an = 7n - 4

Equating the nth terms of both APs since they are equal

61 + 2n = 7n - 4

⇒ 61 + 4 = 7n - 2n

⇒ 65 = 5n

⇒ n = 655 = 13

Result:

The 13th terms of both APs are equal.

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