Question

If the $3^{\text{rd}}$ and $6^{\text{th}}$ terms of a G.P are 12 and 96, then its common ratio is ___.

• A. 4
• B. 9
• C. 2
• D. 7

Answer 1

The correct option is C

2

Given: $t_3=12t_6=96$

The $n^{\text{th}}$ term of a GP of first term $a$ and common ratio $r$ is given by
$T_n=a\times r^{(n-1)}.$

$\Rightarrow a{r}^{3-1}=12\text{and}a{r}^{6-1}=96$

i.e., $a{r}^2=12---\left(1\right)$

$a{r}^5=96---\left(2\right)$

Dividing equation (2) by (1), we get

$\frac{a{r}^5}{a{r}^2}=\frac{96}{12}$

$\Rightarrow r^3=8$

$\Rightarrow r=2$
Thus, the common ratio of the GP is 2.