what is the common ratio of the sequence? -2, 6, -18, 54,... -3 -2 3 8

Explanation:

Step1: Recall common - ratio formula

The common ratio $r$ of a geometric sequence is given by $r=\frac{a_{n + 1}}{a_{n}}$, where $a_{n+1}$ is the $(n + 1)$ - th term and $a_{n}$ is the $n$ - th term.

Step2: Calculate the common ratio

Let's take the second term $a_{2}=6$ and the first term $a_{1}=-2$. Then $r=\frac{a_{2}}{a_{1}}=\frac{6}{-2}=-3$. We can double - check with other consecutive terms. For example, if we take the third term $a_{3}=-18$ and the second term $a_{2}=6$, then $r = \frac{a_{3}}{a_{2}}=\frac{-18}{6}=-3$. Also, if we take the fourth term $a_{4}=54$ and the third term $a_{3}=-18$, then $r=\frac{a_{4}}{a_{3}}=\frac{54}{-18}=-3$.

Answer:

A. -3