Question

Find the sum of the following infinite G.P. :

$\frac{1}{3},\frac{-2}{9},\frac{4}{27},\frac{-8}{81},...$

• A. $\frac{1}{2}$
• B. $1$
• C. $\frac{1}{3}$
• D. $\frac{1}{5}$

Answer 1

Answer: (D)

$\frac{1}{5}$

Here, $a=\frac{1}{3},r=\frac{\frac{-2}{9}}{\frac{1}{3}}=-\frac{2}{3}$

Hence, the required sum = $\frac{a}{1-r}=\frac{\frac{1}{3}}{1-(-\frac{2}{3})}=\frac{1}{5}$