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.$a$, if $a_n = 28, S_n = 144$ and $n = 9$.

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 $a$, if $a_n = 28, S_n = 144$ and $n = 9$.

Solution:

$a_n=l=28$

We know that,

$\mathrm{S}_{n}=\frac{n}{2}[a+l]$

$S_n=\frac{9}{2}[a+28]$

$144(2)=9(a+28)$

$16(2)=a+28$

$a=32-28$

$a=4$

Therefore, $a=4$.