Let there be an A.P. with first term ‘$a$’, common difference '$d$'. If $a_n$ denotes its $n^{th}$ term and $S_n$ the sum of first $n$ terms, find.$d$, if $a = 3, n = 8$ and $S_n = 192$.

Given:

In an A.P., first term $=a$ and common difference $=d$.

$a_n$ denotes its $n^{th}$ term and $S_n$ the sum of first $n$ terms.

To do:

We have to find $d$, if $a = 3, n = 8$ and $S_n = 192$.

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, $d=6$.