# What are the next three terms in the sequence 12, 4, 3/4 ?

Mar 24, 2016

This looks like a geometric sequence with common ratio $\frac{1}{3}$, with an error in the third term, which should be $\frac{4}{3}$ rather than $\frac{3}{4}$.

If so, then the next $3$ terms are: $\frac{4}{9}$, $\frac{4}{27}$, $\frac{4}{81}$

#### Explanation:

With only three terms, about the only pattern which makes sense is if the third term should be $\frac{4}{3}$ rather than $\frac{3}{4}$.

If this is so, then this is a geometric sequence with initial term $12$ and common ratio $\frac{1}{3}$.

The terms of a geometric sequence are given by the formula:

${a}_{n} = a {r}^{n - 1}$

where $a$ is the initial term and $r$ the common ratio.

In our case, $a = 12$, $r = \frac{1}{3}$ and the general term is given by:

${a}_{n} = 12 {\left(\frac{1}{3}\right)}^{n - 1}$

So the sequence starts:

$12 , 4 , \frac{4}{3} , \frac{4}{9} , \frac{4}{27} , \frac{4}{81} , \ldots$