Question

Calculate the sum of first $20$ terms of the G.P. $-1,1,-1,\mathrm{1....}$

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

Answer: (A)

$0$

Given series is $-1,1,-1,1,....$

Here $a=-1,r=-1$

We know the formula, $S_n=\frac{a_1(1-r^n)}{1-r}$
$S_{20}=\frac{1(1-(-1{)}^{20})}{1-(-1)}$
$=\frac{1(1-(-1{)}^{20})}{2}$
$=0$