Question

Find sum of the series $-2,2\frac{1}{2},-3\frac{1}{8},...$ upto $6$ terms.

Answer 1

Number of terms $n=6$
First term $=a=-2$
Common ratio $=r=\frac{-5}{4}$
Formula for sum of $n$ terms of G.P. is given by

$S_n=\frac{a(r^n-1)}{r-1}$
$S_6=\frac{(-2)({\left(\frac{-5}{4}\right)}^6-1)}{\frac{-5}{4}-1}$
$S_6=\frac{\left(8\right)({\left(\frac{5}{4}\right)}^6-1)}{9}$

$S_6=\frac{1281}{512}$