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

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 $3,6,12, \ldots$

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