Question

The sum of an infinite GP is 162 and the sum of its first n terms is 160. If the inverse of its common ratio is an integer, then how many values of common ratio is/are possible, common ratio is greater than 0?

• A. 1
• B. 2
• C. 3

Answer 1

The correct option is C 3

$\frac{a}{(1-r)}=162anda\frac{(1-r^n)}{1-r}=160\Rightarrow 1-r^n=\frac{160}{162}\Rightarrow r^n=\frac{1}{81}$
Hence, there will be three values of 1/r, i.e. 3, 9, and 81.