Question

Write the value of n for which nth terms of the A.P.s 3, 10, 7, ... and 63, 65, 67, .... are equal.

Answer 1

We have,

3 + 10 + 17 + ...

$\Rightarrow a_n=3+(n-1)7$

and 63, 65, 67 ... .... (i)

$[\because a_n=a+(n-1\left)d\right]$

$\Rightarrow a_n^{{}^{\prime }}=63+(n-1)2\dots \dots \left(ii\right)$

It is given that

$a_n=a_n^{{}^{\prime }}$

$\Rightarrow 3+(n-1)7=63+(n-1)2$

$\Rightarrow 3+7n-7=63+2n-2$

$\Rightarrow 7n-2n=61+4$

$\Rightarrow 5n=65$

$\Rightarrow n=13$