Question

The sum of an infinite G.P. with positive terms is $48$ and sum of its first two terms is $36.$ Find the second term.

• A. $10$
• B. $18$
• C. $12$
• D. $20$

Answer 1

The correct option is C $12$

Let $a$ be the first term and $r$ be the common ratio of the G.P.

We have,

$\frac{a}{1-r}=48$

$a=48(1-r)$ .....(1)

Also, it is given that $a+ar=36$

$48(1-r)(1+r)=36$

$1-r^2=\frac{3}{4}$

$r^2=\frac{1}{4}$

$r=\pm \frac{1}{2}$

When $r=\frac{1}{2},a=48\times \frac{1}{2}=24$ and the second term = $ar=24\times \frac{1}{2}=12$

When $r=-\frac{1}{2}$, the terms of the G.P. will become negative.

So, the second term is $12.$