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