What is the sum of the first 11 terms of an arithmetic progression if the 3^rd term is -1 and the 8^th term is 19?

Solution (By Examveda Team)

$$\eqalign{ & {T_3} = a + 2d = - 1.....\,\left( 1 \right) \cr & {T_8} = a + 7d = 19\,.....\,\left( 2 \right) \cr & {\text{on solving}}\left( 1 \right)\,{\text{and}}\,\left( 2 \right) \cr & d = 4\,\& \,a = - 9 \cr & {S_n} = \frac{n}{2}\left[ {2a + \left( {n - 1} \right)d} \right] \cr} $$
$${S_{11}} = \frac{{11}}{2}$$ $$\left[ {2\left( { - 9} \right) + \left( {11 - 1} \right)\left( 4 \right)} \right]$$
$$\eqalign{ & {S_{11}} = \frac{{11}}{2}\left[ {\left( { - 18} \right) + \left( {40} \right)} \right] \cr & {S_{11}} = \frac{{11}}{2}\left[ {22} \right] \cr & {S_{11}} = 121 \cr} $$