Question

The third term of an A.P. is 7 and its $7^{th}$ term is 2 more than thrice of its $3^{rd}$ term. Find the common difference .

Answer 1

The third term of an A.P. is $a+2d$ where $a$ is the first term and $d$, the common difference.
So, $a+2d=7$
The next given condition says $a+6d=21+2=23$
Solving simultaneously, we have $4d=23-7=16$
$\Rightarrow d=4$.