# How do you find the explicit formula for the following sequence 1/3,2/9,4/27,8/81,16/243......?

##### 1 Answer
Feb 15, 2016

${a}_{n} = \frac{1}{3} \cdot {\left(\frac{2}{3}\right)}^{n}$

#### Explanation:

${a}_{0} = \frac{1}{3}$
${a}_{1} = {a}_{0} \cdot \frac{2}{3} = \frac{2}{9}$
${a}_{2} = {a}_{1} \cdot \frac{2}{3} = {a}_{0} \cdot {\left(\frac{2}{3}\right)}^{2} = \frac{4}{27}$
${a}_{3} = {a}_{2} \cdot \frac{2}{3} = {a}_{0} \cdot {\left(\frac{2}{3}\right)}^{3} = \frac{8}{81}$
${a}_{4} = {a}_{3} \cdot \frac{2}{3} = {a}_{0} \cdot {\left(\frac{2}{3}\right)}^{4} = \frac{16}{243}$

$\textcolor{b l a c k}{\text{...}}$

${a}_{n} = {a}_{0} \cdot {\left(\frac{2}{3}\right)}^{n} = \frac{1}{3} \cdot {\left(\frac{2}{3}\right)}^{n}$