Question

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

$2,-6,18,-54,162,-486,...$

Short answer

The sequence is geometric with common ratio equal to$-3$.

Step-by-step solution

Step 1. Given information

The sequence is$2,-6,18,-54,162,-486,...$

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

Consider the sequence $2,-6,18,-54,162,-486,...$

$\begin{array}{rcl}\frac{-6}{2}& =& -3\\ \frac{18}{-6}& =& -3\\ \frac{-54}{18}& =& -3\\ \frac{162}{-54}& =& -3\\ \frac{-486}{162}& =& -3\end{array}$

So, the sequence is geometric with common ratio equal to$-3$.