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

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Solution: We have given 63, 65, 67, …

a = 63

d = a 2 − a 1 = 65 − 63 = 2

n th term of this A.P. = a n a + (n − 1) d

an = 63 + (n − 1) 2 = 63 + 2n − 2

an = 61 + 2n (1)

3, 10, 17, …

a = 3

d = a 2 − a 1 = 10 − 3 = 7

n th term of this A.P. = 3 + (n − 1) 7

an = 3 + 7n − 7

an = 7n − 4 (2)

It is given that, n th term of these A.P.s are equal to each other.

Equating both these equations, we obtain

61 + 2n = 7n − 4

61 + 4 = 5n

5n = 65

n = 13

Therefore, 13th terms of both these A.P.s are equal to each other.

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