Question

Find the sum of $51$ terms of the A.P whose second term is $2$ and fourth term is $8$.

Answer 1

Given,

$a_2=a+d=2$

$a_4=a+3d=8$

solving the above 2 equations, we get,

$d=3,a=-1$

$S_{51}=\frac{51}{2}[2\times (-1)+50\times 3]$

$=\frac{51}{2}\times 2[-1+75]$

$=3774$