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 sum of first term and 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 $4d=23-7=16$
$\Rightarrow d=4$. Thus, $a=7-8=-1$

$\therefore a+d=4-1=3$