Question

If the sum of the first two terms of a G.P is $\frac{9}{2}$ and the sixth term is 8 times the third term , find G.P

Answer 1

Given,

$a+ar=\frac{9}{2}$

$a(1+r)=\frac{9}{2}$

6th term is 8 times the 3rd term

$a{r}^5=8a{r}^2$

$r^3=8$

$\therefore r=2$

$a(1+r)=\frac{9}{2}\Rightarrow a(1+2)=\frac{9}{2}$

$\therefore a=\frac{3}{2}$

Therefore the G.P. series is, $a,ar,a{r}^2,........$

$\frac{3}{2},3,6,.......$