Question

The first two terms of a geometric progression add up to $12$ the sum of the third and the fourth terms is $48$ . If the terms of the geometric progression are alternately positive and negative, then the first term is

• A. -4
• B. -12
• C. 12
• D. 4

Answer 1

Answer: (B)

As per question, $a+ar=12\dots (i)$
$a{r}^2+a{r}^3=48\dots (ii)$
$\Rightarrow \frac{a{r}^2(1+r)}{a(1+r)}=\frac{48}{12}$
$\Rightarrow r^2=4$,
$\Rightarrow r=-2$
$\Rightarrow a=-12$
$(\because$ terms are + ve and - ve alternately )