The sum of first two terms of Geometric Progression is 12 and the sum of third and fourth terms is 48. If the terms of Geometric Progression are alternatively positive and negative, then first term is

 Let a be the first term and  $r$ be the common ratio of Geometric Progression (G.P)

Since the sum of the first and second terms in G.P is 12 

$\begin{array}{l}\Rightarrow a+ar=12\\ \Rightarrow a(1+r)=12\dots \dots \left(1\right)\end{array}$

Since the sum of the third and fourth terms in G.P. is 48

$\Rightarrow a{r}^2+a{r}^3=48$

$\Rightarrow a{r}^2(1+r)=48\dots \dots \left(2\right)$

$\text{ Solving (1) and (2), we get }r=\pm 2$

$\text{ If }r=2,\text{ then }a=4$

$\text{ If }r=-2\text{ and }a=-12$

$\text{ If }r=2\text{ , first two terms are }4,8\text{ . }$

$\text{ If }r=-2\text{ , first two terms are }-12,24\text{ . }$

$\therefore \text{ First term, }a=-12\text{ . }$