For what value of $n$ the $n^{t h}$ term of the following two $A . P . s$ are equal?

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Solution

Let $I^{s t} A . P . 63, 65, 67.........$

We know that $a = 63 d = 2$

$\begin{matrix} a_{n} = a + (n - 1) d = 63 + (n - 1) 2 = 63 + 2 n - 2 = 2 n + 61 \end{matrix}$

Let $2^{n d}$ A.P. is $3, 10, 17........$

$a = 3, d = 7$

$\begin{matrix} a_{n} = a + (n - 1) d = 3 + (n - 1) 7 = 3 + 7 n - 7 = 7 n - 4 I^{s t} A . P . = 2^{n d} A . P . 61 + 2 n = 7 n - 4 61 + 4 = 7 n - 2 n 65 = 5 n n = 13 \end{matrix}$

Hence, this is the answer.

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