Question

The first and the last terms 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

From the question it is give that,

First term $a=17$

Last term $=350$

Common difference $d=9$

We know that, $T_n=a+(n-1)d$

$\begin{array}{c}350=17+(n-1)\times 9\\ 350-17=9n-9\\ 333+9=9n\\ 342=9n\\ n=342/9\end{array}$

$n=38$

$\begin{array}{cc}{S}_n& =\left(n/2\right)(2a+(n-1\left)d\right)\\ & S_{38}=\left(38/2\right)\left(\right(2\times 17)+(38-1\left)d\right)\\ & =19(34+(37\times 9\left)\right)\\ & =19(34+333)\\ & =19\times 367\\ & =6973\end{array}$