Write the value of n for which nth terms of the A.P.s 3, 10, 17, ... and 63, 65, 67, .... are equal.

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Solution

For the first series, a = 3, $d_{1}$ = 7
For the second series, b = 63, $d_{2}$ = 2

Given:
$a_{n} = b_{n} \Rightarrow a + (n - 1) d_{1} = b + (n - 1) d_{2} \Rightarrow 3 + (n - 1) 7 = 63 + (n - 1) 2 \Rightarrow 3 + 7 n - 7 = 63 + 2 n - 2 \Rightarrow 5 n = 65 \Rightarrow n = 13$

Hence, the 13th terms of both the series are the same.

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