Question

Find a GP for which the sum of first two terms is $-4$ and the fifth term is $4$ times the third term

• A. $4,8,16,32,64,......$
• B. $4,-8,16,-32,64,......$
• C. $\frac{4}{3},-\frac{8}{3},-\frac{16}{3},\frac{32}{3},-\frac{64}{3}$
• D. $-\frac{4}{3},-\frac{8}{3},-\frac{16}{3},-\frac{32}{3},-\frac{64}{3}$

Answer 1

Answer: (B), (D)

The correct options are
B $4,-8,16,-32,64,......$
D $-\frac{4}{3},-\frac{8}{3},-\frac{16}{3},-\frac{32}{3},-\frac{64}{3}$

Let the GP is $a,ar,a{r}^2...........$

Given, $a+ar=-4$

$\Rightarrow a(1+r)=-4$

Also given, $a{r}^4=4a{r}^2$

$\Rightarrow r^2=4$

$\Rightarrow r=\pm 2$

For $r=2$, $a=\frac{-4}{3}$

Then series will be $\frac{-4}{3},\frac{-8}{3},\frac{-16}{3},......$

For $r=-2$, $a=4$

Then series will be, $4,-8,16,-32,.........$