# How do you write a geometric sequence with a common ratio of 2/3?

Oct 24, 2016

Geometric sequence is $\left\{{a}_{1} , \frac{2}{3} {a}_{1} , \frac{4}{9} {a}_{1} , \frac{8}{27} {a}_{1} , \ldots . , {\left(\frac{2}{3}\right)}^{n - 1} {a}_{1}\right\}$

#### Explanation:

Common ratio of $\frac{2}{3}$ means that a succeeding number is $\frac{2}{3}$ times the preceding number.

Here if the first number of the geometric sequence is ${a}_{1}$,

second number ${a}_{2}$ is ${a}_{1} \times \frac{2}{3}$

third number is given by ${a}_{3} = {a}_{1} \times {\left(\frac{2}{3}\right)}^{2}$

and ${n}^{t h}$ number is ${a}_{n} = {a}_{1} \times {\left(\frac{2}{3}\right)}^{n - 1}$

and geometric sequence is $\left\{{a}_{1} , \frac{2}{3} {a}_{1} , \frac{4}{9} {a}_{1} , \frac{8}{27} {a}_{1} , \ldots . , {\left(\frac{2}{3}\right)}^{n - 1} {a}_{1}\right\}$