Question

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

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

Answer 1

The correct option is A $\frac{1}{3}$

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 $a{r}^7=54$
$\Rightarrow \frac{a{r}^7}{a{r}^4}=\frac{54}{1458}$
$\Rightarrow r^3=\frac{1}{27}$
$\Rightarrow r=\frac{1}{3}$