Question

The first term and the last term of an A.P are $17$ and $350$ respectively. If the common difference is $9$. How many terms are there and what is their sum.

Answer 1

$a_1=17,a_n=350,d=9$

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

$350=17+9(n-1)$
$333=9(n-1)$
$n-1=37$

$n=38$

So, sum, $S_n=\frac{n}{2}(a+l)\Rightarrow S_{38}=\frac{38}{2}(17+350)$

$=19\times 367$

$=6973$