# Find the explicit formula for the following sequence 1/3,2/9,4/27,8/81,16/243....

Find the explicit formula for the following sequence 1/3,2/9,4/27,8/81,16/243....
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Skye Hamilton
${a}_{0}=\frac{1}{3}$
${a}_{1}={a}_{0}\cdot \frac{2}{3}=\frac{2}{9}$
${a}_{2}={a}_{1}\cdot \frac{2}{3}={a}_{0}\cdot {\left(\frac{2}{3}\right)}^{2}=\frac{4}{27}$
${a}_{3}={a}_{2}\cdot \frac{2}{3}={a}_{0}\cdot {\left(\frac{2}{3}\right)}^{3}=\frac{8}{81}$
${a}_{4}={a}_{3}\cdot \frac{2}{3}={a}_{0}\cdot {\left(\frac{2}{3}\right)}^{4}=\frac{16}{243}$
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${a}_{n}={a}_{0}\cdot {\left(\frac{2}{3}\right)}^{n}=\frac{1}{3}\cdot {\left(\frac{2}{3}\right)}^{n}$