Question

In an A.P the first term is $25$, $n$th term is $-17$ and the sum of first $n$ terms is $60$. Find the common difference.

Answer 1

We know

$S_n=\frac{n}{2}[a+a_n]$

$60=\frac{n}{2}[25+(-17\left)\right]$

$60=\frac{n}{2}\left[8\right]$

$n=\frac{60\times 2}{8}$

$n=15$

Now,

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

$-17=25+(15-1)d$

$-17-25=14d$

$d=\frac{-42}{14}$

$d=-3$

Therefore common difference is -3.