Recognizing Geometric Sequences

By observing the change that occurs between consecutive terms, we can describe the pattern of the given geometric sequence. Here, we see that the common ratio from one term to the next is $\text{-}3.$ $$\begin{array}{r}\text{-}7\stackrel{\times (\text{-}3)}{\to }21\stackrel{\times (\text{-}3)}{\to }\text{-}63\end{array}$$ To find the next three terms in the sequence, we will extend this pattern three times. $$\begin{array}{r}21\stackrel{\times (\text{-}3)}{\to }\text{-}63\stackrel{\times (\text{-}3)}{\to }189\stackrel{\times (\text{-}3)}{\to }\text{-}567\stackrel{\times (\text{-}3)}{\to }1701\end{array}$$