The $7^{t h}$ term of a G.P. is $8$ times the $4^{t h}$ term. Find the G.P. When its $5^{t h}$ term is $48$

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Solution

Given that $t_{7} = 8 t_{4} \Rightarrow a r^{6} = 8 a r^{3}$
$\Rightarrow r^{3} = 8 = 23 \Rightarrow r = 2$
Also $t_{5} = 48 \Rightarrow a r^{4} = 48$ or $16 a = 48 \Rightarrow a = 3$ .
Hence the required G.P. is $3, 6, 12, 24 . . . . . . . . . .$

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