Chapter 7.8, Problem 13P

Find the common ratio for each geometric sequence.

$2,-6,18,-54,\dots$

To determine

To find : the common ratio for the geometric sequence.

Answer to Problem 13P

  $-3$

Explanation of Solution

Given sequence: $2,-6,18,-54,\mathrm{......}$

Calculation:

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed , non-zero number called common ratio.

Therefore, common ratio r for a geometric sequence is obtained by dividing any term in the sequence by the previous term.

The common ratio for given geometric sequence is

  $\begin{array}{l}r=\frac{a_2}{a_1}\\ r=\frac{-6}{2}=-3\end{array}$

Thus, common ratio for given geometric sequence is $-3$ .