Question

The fifth and fifteenth term of an $A.P.$ are $13$ and $-17.$ find sum of first $21$ terms of an $A.P.$

Answer 1

Given,

$a_5=a+4d=13$.....(1)

$a_{15}=a+14d=-17$.......(2)

solving (1) and (2), we get,

$d=-3$

From (1), we get,

$a=25$

$S_{21}=\frac{21}{2}\left[2\right(25)+(21-1\left)\right(-3\left)\right]$

$=\frac{21}{2}[50-60]$

$=-105$