Question

If the first term and the last term of a finite $A.P.$ are $5$ and $95$ respectively and $d=5,$ find $n$ and $S_n.$

Answer 1

$a=5$

$a_n=95$

$d=5$

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

$\Rightarrow 95=5+(n-1)5$

$19=1+n-1$

$n=19$

$\Rightarrow S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

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

$=\frac{n}{2}[5+95]$

$=19\times 50=950$