Question

The seventh term of a G.P. is 8 times the fourth term and 5th term is 48. Find the G.P.

Answer 1

Let a be the first term and r be the common ratio.

$\therefore a_7=8a_{4}and{a}_5=48$

$\Rightarrow a{r}^6=8a{r}^{3}anda{r}^4=48$

$\Rightarrow r^3=8$

$\Rightarrow r^3=2^3$

$\Rightarrow r=2$

Putting $r=2ina{r}^4=48$

$a(2{)}^4=48$

$\Rightarrow a=3$

Thus, the given G.P. is 3, 6, 12, .....