Question

The first two terms of G.P. add upto $12$. The sum of $3^{rd}$ and $4^{th}$ term is $48$. If the terms of G.P. are alternating positive and negative then the first terms is

Answer 1

Let the first terms be $a,ar,a{r}^2,a{r}^3..$

From the given conditions

$r<0$

$a(1+r)=12$

$a{r}^2+a{r}^3=48⟹r^2=4⟹r=-2⟹a=-12$

The first terms are $-12,24,-48,96,..$