Chapter 8.5, Problem 106E

To determine

To check: if the sequence is arithmetic, geometric or neither with explanation.

Answer to Problem 106E

Geometric sequence.

Explanation of Solution

Given information: We have given a sequence $-2,-6,-18,-54,\mathrm{...........}$

We need to check for the ratios of next terms to previous terms to determine if it is a geometric sequence.

  $\begin{array}{l}{r}_1=\frac{a_2}{a_1}=\frac{-6}{-2}=3\\ r_2=\frac{a_3}{a_2}=\frac{-18}{-6}=3\\ r_3=\frac{a_4}{a_3}=\frac{-54}{-18}=3\end{array}$

We could see that ratios of next terms to previous terms are same. So, it’s a Geometric sequence.

Therefore, the given sequence is a geometric sequence.