# The common ratio in a geometric sequence is 3/2, and the fifth term is 1. How do you find the first three terms?

May 22, 2016

$\frac{16}{81}$, $\frac{8}{27}$, $\frac{4}{9}$

#### Explanation:

The formula for finding the ${n}^{\text{th}}$ ( ${U}_{n}$) term in a geometric sequence is

${U}_{n} = {U}_{1} \times {r}^{\text{n-1}}$

where $r$ is the common ratio.

U_1 = ?
${U}_{5} = 1$
$r = \frac{3}{2}$

${U}_{5} = {U}_{1} \times {\left(\frac{3}{2}\right)}^{\text{5-1}}$

$1 = {U}_{1} \times {\left(\frac{3}{2}\right)}^{\text{4}}$

Rearrange

$\frac{1}{\frac{3}{2}} ^ \text{4} = {U}_{1}$

${U}_{1} = \frac{1}{\frac{81}{16}} = \frac{16}{81}$

${U}_{2} = \frac{16}{81} \times \frac{3}{2} = \frac{8}{27}$

${U}_{3} = \frac{8}{27} \times \frac{3}{2} = \frac{4}{9}$