Question

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

• A. $12$
• B. $4$
• C. $-4$
• D. $-12$

Answer 1

The correct option is D $-12$

let the terms be $a,ar,a{r}^2,a{r}^3$
sum of first two terms is 12. $\Rightarrow a+ar=12$
sum of third and fourth terms is 48. $\Rightarrow a{r}^2+a{r}^3=48$
now dividing both the equations we get $r^2=4$
$r=-2$ (as the common ratio should be negative as the terms given are alternatively positive and negative!)
and then substituting $r=-2$ in $a+ar=12$, we get $a=-12$