Question

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

$-3,6,-12,24,-48,96,...$

Short answer

The sequence is geometric with common ratio equal to$-2$.

Step-by-step solution

Step 1. Given information

The sequence is$-3,6,-12,24,-48,96,...$.

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

Consider the sequence $-3,6,-12,24,-48,96,...$

$\begin{array}{rcl}\frac{6}{-3}& =& -2\\ \frac{-12}{6}& =& -2\\ \frac{24}{-12}& =& -2\\ \frac{-48}{24}& =& -2\\ \frac{96}{-48}& =& -2\end{array}$

So, the sequence is geometric with common ratio equal to$-2$.