Question

In an $A.P.$, the ${19}^{th}$ term is $52$ and ${38}^{th}$ term is $128$, find sum of first $56$ terms.

Answer 1

$19thterm=a+18d=52$......(1)

$30thterm=a+37d=128$......(2)

$\left(2\right)-\left(1\right)\Rightarrow 19d=76$

$=d=4$

$=a=-20$

$S_{56}=\frac{n}{2}[2a+(n-1\left)d\right]$

$=\frac{56}{6}\left[\right(2(-20)+55\times 4]$

$=28[-40+220]$

$=20\times 180=5040$