Question

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

Answer 1

In the first AP,
$a=63d=2T_n=63+(n-1)\times 2=2n+61$

In the second AP,
$a=3d=7T_n=3+(n-1)\times 7=7n-4$

Now, $7n-4=2n+61\Rightarrow 5n=65\Rightarrow n=13$