Question

How many terms of the A.P. $18,16,14,.....$ be taken, so that their sum is zero?

Answer 1

First term, $a=18$; common difference, $d=16-18=-2$

$n^{th}$ terms sum is given by $S_n=\frac{n}{2}(20+(n-1\left)d\right)=0$

$\Rightarrow 2a+(n-1)d=0$

$\Rightarrow 36-2(n-1)=0$

$\Rightarrow 36=2n-2$

$\Rightarrow 2n=32$

$\Rightarrow n=19$.

or, $n=16$.