How do you write the first five terms of the sequence a_n=2^n/3^n?

May 5, 2018

$\left\{{a}_{n}\right\} = \left\{\frac{2}{3} , \frac{4}{9} , \frac{8}{27} , \frac{16}{81} , \frac{32}{243}\right\}$

Explanation:

${a}_{n} = {2}^{n} / {3}^{n}$

${a}_{1} = {2}^{1} / {3}^{1} = \frac{2}{3}$

${a}_{2} = {2}^{2} / {3}^{2} = \frac{4}{9}$

${a}_{3} = {2}^{3} / {3}^{3} = \frac{8}{27}$

${a}_{4} = {2}^{4} / {3}^{4} = \frac{16}{81}$

${a}_{5} = {2}^{5} / {3}^{5} = \frac{32}{243}$

$\left\{{a}_{n}\right\} = \left\{\frac{2}{3} , \frac{4}{9} , \frac{8}{27} , \frac{16}{81} , \frac{32}{243}\right\}$