Question

The first and the last terms of an arithmetic progression are $17$ and $350$. Also the common difference of the A.P. is $9$. Find the number of terms in the A.P. and also find the sum of the terms.

Answer 1

$a=17l=350d=9a_n=a(n-1)d350=17+(n-d)9\frac{333}{9}=(n-1)37=n-1n=38s_n=\frac{n}{2}[2a+(n-1\left)d\right]s_n=\frac{38}{2}[34+(38-1\left)9\right]s_n=6973$