Question

What is the sum of the following series ? -64, -66, -68,. ., -100​

Answer 1

Recall the concept of arithmetic series

The equation for A.P is $a_n=a+(n-1)d$ where $a$ is the first term, $n$ is the number of terms, $d$ is the common difference, $a_n$ is the $n^{th$ term

The sum of terms in AP is given by $S_n=\frac{n}{2} [2a+(n-1)d]$

Given: $-64, -66, -68,......-100$

$a=-64; d=-2; a_n=-100$

Explanation:

The number of terms can be calculated by

$a_n=a+(n-1)d$

$\implies -100=-64+(n-1)-2$

$\implies -100+64=(n-1)-2$

$\implies \frac{-36}{-2}=(n-1)$

$\implies 18=n-1$

$\implies n=19$

The sum of the $19$ terms of the series

$S_n=\frac{n}{2} [2a+(n-1)d]$

$\implies S_{19}=\frac{19}{2} [2(-64)+(19-1)(-2)]$

$\implies S_{19}=\frac{19}{2} [2(-64)+18(-2)]$

$\implies S_{19}=\frac{19}{2} [-164]$

$\implies S_{19}=19 \times-82$

$\implies S_{19}=-1558$