# How do you find the missing term in the geometric sequence 9/4, 3/4, 1/4, 1/12, __?

Dec 18, 2016

Missing term is $\frac{1}{36}$

#### Explanation:

In the given geometric sequence $\left\{\frac{9}{4} , \frac{3}{4} , \frac{1}{4} , \frac{1}{12} , -\right\}$, let us first the common ratio $r$, which is the ratio between a term and its preceding term.

Note that it means that succeeding term is peceding term multiplied by common ratio.

$r = \frac{\frac{1}{12}}{\frac{1}{4}} = \frac{\frac{1}{4}}{\frac{3}{4}} = \frac{\frac{3}{4}}{\frac{9}{4}}$ or

$r = \frac{1}{12} \times \frac{4}{1} = \frac{1}{4} \times \frac{4}{3} = \frac{3}{4} \times \frac{4}{9} = \frac{1}{3}$

Hence, the last missing term is $\frac{1}{12} \times \frac{1}{3} = \frac{1}{36}$