# How do you find the next two terms of the geometric sequence 1/3, 5/6, 25/12,...?

##### 1 Answer
Oct 23, 2016

The next two terms are found by multiplying by the common ratio $r = \frac{5}{2}$ which results in $\frac{125}{24}$ and $\frac{625}{48}$.

#### Explanation:

A geometric sequence is a sequence of numbers generated by mutiplying the previous term by the common ratio or $r$.

Find the common ration $r$ by dividing any term by the previous term.

In this example, $r = \frac{5}{6} \div \frac{1}{3} = \frac{5}{2}$.

The second term is generated by multiplying the first term by $\frac{5}{2}$
or $\frac{1}{3} \cdot \frac{5}{2} = \frac{5}{6}$

The third term is generated by multiplying the second term by $\frac{5}{2}$ or $\frac{5}{6} \cdot \frac{5}{2} = \frac{25}{12}$

Similarly, the fourth term is $\frac{25}{12} \cdot \frac{5}{2} = \frac{125}{24}$

The fifth term is $\frac{125}{24} \cdot \frac{5}{2} = \frac{625}{48}$