In an AP:
Given $a = 3, n = 8, S = 192$, find $d$.

Given:

In an A.P., $a = 3, n = 8, S = 192$.

To do:

We have to find $d$.

Solution:

We know that,

$\mathrm{S}_{n}=\frac{n}{2}[2 a+(n-1) d]$

$S_n=\frac{8}{2}[2 \times 3+(8-1) \times d]$

$192=4[6+7d]$

$48=(6+7d)$

$7d=48-6$

$7d=42$

$d=\frac{42}{7}$

$d=6$

Therefore, $d=6$.