Question

Find a G.P for which sum of the first two terms is -4 and the fifth term is 4 times the third term.

Answer 1

Let 'a' be the first term and 'r' be the common ratio of given G.P,

Here a + ar = - 4

$\therefore a(1+r)=-4$ ........(i)

and $a_5=4a_3$

$\therefore a{r}^4=4a{r}^2\Rightarrow r^2=4\Rightarrow r=\pm 2$

When r = 2, then putting the value of r is (i),

$a(1+2)=-4\Rightarrow a=-\frac{4}{3}$

Thus, the required G.P. is $\frac{-4}{3},\frac{-8}{3},\frac{-16}{3},....$

When r = - 2, then putting the value of r in (i)

$a(1-2)=-4\Rightarrow a=4$

Thus, the required G.P. is 4, - 8 , 16, -32, ....