Question

The sum of first two terms of a geometric progression is 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. 4
• D. 12

Answer 1

Answer: (B)

Let $a,ar,a{r}^2,a{r}^3$ ......
$a+ar=12$ ......(I)
$a{r}^2+a{r}^3=48$ .......(II)
(I) $÷$ (II) $\frac{a(1+r)}{a{r}^2(1+r)}=\frac{12}{48}\Rightarrow \frac{1}{r^2}=\frac{1}{4}$
$r=\pm 2$
Terms altemately positive and negative
$\therefore r=-2$
From equation (I) $-a=12\Rightarrow a=-12$.