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Q.

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

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a

13

b

10

c

14

d

11

answer is A.

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Detailed Solution

The formula for n th 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 is 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......... (1)
By Simplifying equation (1)
7(n - 1) - 2(n - 1) = 63 - 3
7n - 7 - 2n + 2 = 60
5n - 5 = 60
n =

\frac{65}{5}

n = 13
The 13th term of the two given APs is equal.
So, option 1 is correct.

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