Question

The sum of the first three terms of the G.P. in which the difference between the second and the first term is 6 and the difference between the fourth and the third term is 54, is

• A. 39
• B. - 10.5
• C. 27
• D. - 27

Answer 1

Answer: (A), (B)

$a,ar,a{r}^2,a{r}^3$
$ar-a\Rightarrow 6\Rightarrow a(r-1)=6$....(1)
$a{r}^2-a{r}^2=54\Rightarrow {\mathrm{ar}}^2(r-1)=54$....(2)
(2) $/(1)\Rightarrow r^2=9$ or $r=\pm 3$
when $r=3$ and $a=3$ when $r=-3$ and $a=-3/2$
a, ar,$a^2$ a, ar, $a{r}^2$
$3,9,27\Rightarrow$ sum $=39$ $\mathrm{sum}=-3/2(1-3+9)=-21/2=-10.5$.