Question

In the exercise, determine if the sequence is geometric, and if so, indicate the common ratio.

$54,18,6,2,\frac{2}{3},\frac{2}{9},...$

Short answer

The sequence is geometric with common ratio equal to$\frac{1}{3}$.

Step-by-step solution

Step 1. Given information

The sequence is$54,18,6,2,\frac{2}{3},\frac{2}{9},...$

Step 2. Determine if the sequence is geometric, and if so, indicate the common ratio.

Consider the sequence $54,18,6,2,\frac{2}{3},\frac{2}{9},...$

$$\begin{gathered} \frac{18}{54}=\frac{1}{3} \\ \frac{6}{18}=\frac{1}{3} \\ \frac{2}{6}=\frac{1}{3} \\ \frac{{\displaystyle \frac{2}{3}}}{2}=\frac{1}{3} \\ \frac{{\displaystyle \frac{2}{9}}}{{\displaystyle \frac{2}{3}}}=\frac{1}{3} \end{gathered}$$

So, the sequence is geometric with common ratio equal to$\frac{1}{3}$