Question

Find sum of the series $2,-4,8,...$ upto $10$ terms.

Answer 1

Clearly the given series is G.P with common ratio $r=-2$ and first term $a=2$
Also, $n=10$
$S_n$ be sum of first $n$ terms of G.P
Formula for sum of $n$ terms of G .P is given by
$S_n=\frac{a(r^n-1)}{r-1}$

$S_{10}=\frac{2\times \left(\right[-2{]}^{10}-1)}{-2-1}=\frac{-2046}{3}=-682$