Question:
The seventh term of a G.P. is 8 times the fourth term and 5th term is 48. Find the G.P.
Solution:
Let $a$ be the first term and $r$ be the common ratio.
$\therefore a_{7}=8 a_{4}$ and $a_{5}=48$
$\Rightarrow a r^{6}=8 a r^{3}$ and $a r^{4}=48$
$\Rightarrow r^{3}=8$
$\Rightarrow r^{3}=2^{3}$
$\Rightarrow r=2$
Putting $r=2$ in $a r^{4}=48$
$a(2)^{4}=48$
$\Rightarrow a=3$
Thus, the given G.P. is $3,6,12, \ldots$