Question

If ninth term of an A.P. is $20$, find the sum of its seventeen term.

Answer 1

Let $a$ be the first term and $d$ be the common difference of the A.P.

Then according to the problem, $a+8d=20$......(1).

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

Now, the sum of $17$ th term is $=\frac{17}{2}\times (2a+16d)=\frac{17}{2}\times 2\times 20=340.$ [ Using (1)].