How many terms of the sequence 18, 16, 14, ..... should be taken … - Vidyadip

Question

How many terms of the sequence $18, 16, 14, .....$ should be taken so that sum is zero?

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Answer

Given A.P.
$18, 16, 14, .....$
Sum, $S_n = 0$
Here, First term $a = 18$
and Difference $d = 16 - 18 = -2$
We know,
$\text{S}_\text{n}=\frac{\text{n}}{2}\Big[2\text{a}+(\text{n}-1)\text{d}\Big]$
$\Rightarrow\ 0=\frac{\text{n}}{2}[2(18)+(\text{n}-1)(-2)]$
$\Rightarrow 0 = n[36 - 2n + 2]$
$\Rightarrow 0 = n[38 - 2n]$
$\Rightarrow 0 = 38 - 2n$
$\Rightarrow 2n = 38$
$\Rightarrow n = 19$
Hence, Sum of $19$ terms is zero.

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