What is the sum of the first 12 terms of an arithmetic progression if the 3^rd term is -13 and the 6^th term is -4?

Solution(By Examveda Team)

$$\eqalign{ & {T_3} = a + 2d = - 13\,.....\,\left( 1 \right) \cr & {T_6} = a + 5d = - 4\,.....\,\left( 2 \right) \cr & {\text{on solving}}\left( 1 \right)\,{\text{and}}\,\left( 2 \right) \cr & d = 3\& a = - 19 \cr & {S_n} = \frac{n}{2}\left[ {2a + \left( {n - 1} \right)d} \right] \cr} $$
$${S_{12}} = \frac{{12}}{2}$$ $$\left[ {2\left( { - 19} \right) + \left( {12 - 1} \right)\left( 3 \right)} \right]$$
$$\eqalign{ & {S_{12}} = \left( 6 \right)\left[ { - 38 + 33} \right] \cr & {S_{12}} = - 30 \cr} $$