Chapter 7.8, Problem 9P

Find the common ratio for each geometric sequence.

$-2,4,-8,16,\dots$

To determine

To find : the common ratio for the geometric sequence.

Answer to Problem 9P

  $-2$

Explanation of Solution

Given sequence: $-2,4,-8,16,\mathrm{.......}$

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

  $\begin{array}{l}r=\frac{a_2}{a_1}\\ r=\frac{4}{-2}=-2\end{array}$

Thus, common ratio for given geometric sequence is $-2$ .