Answer
The common ratio is $r=-\frac{1}{3}$.
Work Step by Step
The given sequence is
$-162,54,-18,6,...$
Calculate the ratio between each pair of consecutive terms.
$\frac{54}{-162}=-\frac{1}{3}$
$\frac{-18}{54}=-\frac{1}{3}$
$\frac{6}{-18}=-\frac{1}{3}$
Hence, the common ratio is $r=-\frac{1}{3}$.
