Question

The $5^th$ and $8^{th}$ terms of a $G.P.$ are $1458$ and $54$ respectively. The common ratio of the $G.P.$ is

• A. $\frac{1}{3}$
• B. 3
• C. 9
• D. $\frac{1}{9}$
• E. $\frac{1}{8}$

Answer 1

Answer: (A)

Let $a$ and $r$ be the first term and common ratio of the GP. It is given that,
$a_{5}=1458$ and $a_{8}=54$
$\Rightarrow a r^{4}=1458$ and $a r^{7}=54$
$\Rightarrow \frac{a r^{7}}{a r^{4}}=\frac{54}{1458}$
$\Rightarrow r^{3}=\frac{1}{27} $
$\Rightarrow r =\frac{1}{3}$