Question

Calculate the missing term in the geometric progression $\frac{1}{4},x,\frac{1}{36},\frac{1}{108},.....$.

• A. $\frac{1}{3}$
• B. $\frac{1}{9}$
• C. $\frac{1}{12}$
• D. $\frac{1}{16}$
• E. $\frac{1}{18}$

Answer 1

The correct option is C $\frac{1}{12}$

To find the missing term, we need to find the common ratio between each term.

$\Rightarrow t_n=t_1.r^{n-1}$

$\Rightarrow t_3=\frac{1}{4}{r}^{3-1}$

$\Rightarrow \frac{1}{36}=\frac{1}{4}{r}^2$

$\Rightarrow r^2=\frac{1}{36}\times 4$

$\Rightarrow r^2=\frac{1}{9}$

$\Rightarrow r=\frac{1}{3}$

$\therefore x=\frac{1}{4}\times \frac{1}{3}=\frac{1}{12}$