Question

Find the sum of $25$ terms of an $AP$. Whose $7^{th}$ term is two more than thrice of $370$ terms and $3^{rd}$ term is $7$.

Answer 1

Seventh term $T_7=a+6d$

Third term $T_3=a+2d$

And we have

$T_7=2+3T_3$

so, $a+6d=2+3(a+2d)$

$⟹a=-1$

and $d=3$

Now sum of $25$ terms$=\frac{25}{2}[2\times (-1)+(25-1\left)3\right]=875$