Question

given $a_n=3,n=8,S_n=-192$, find $d$.

Answer 1

Given: $a_n=3$; $n=8$

$S_n=+92$

To find: d

$a_n=a+(n-1)d$

$3=a+7d$ ………..$\left(1\right)$

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

$-192=\frac{8}{2}[2a+7d]$

$2a+7d=-48$ ………..$\left(2\right)$

$a+(a+7d)=-48$

From equation $\left(1\right)$

$a+3=-48$

$a=-51$

Put $a=-51$ in equation $\left(1\right)$

$3=-51+7d$

$7d=54$

$d=\frac{54}{7}$.