Question

In an A.P., the first term is $25$, $n^{th}$ term is $-17$ and the sum of n terms is $132$. Find n and the common difference.

Answer 1

$a=25a+(n-1)d=-17(n-1)d=-42$

Sum$=132$

$\frac{n}{2}(2a+(n-1\left)d\right)=132\frac{n}{2}\left(8\right)=132n=33d=-\frac{21}{16}$

Common difference$=-\frac{21}{16}$