Chapter 7.8, Problem 14PPE

To determine

Todetermine:whether the given sequence is a geometric sequence.

Answer to Problem 14PPE

The sequence $\langle s\rangle =6,-12,24,-48,\dots$ is a geometric sequence.

Explanation of Solution

Given information:

The given sequence is $6,-12,24,-48,\dots$ .

Conceptused:

A sequence of the form $a,ar,a{r}^2,a{r}^3,\dots ,a{r}^{n-1},\dots$ is the geometric with a as the first term, r the common ratio, and nth term $T_n=a{r}^{n-1}$ .

A geometric sequence is a sequence in which the ratio consecutive terms is constant.

The given sequence is $\langle s\rangle =6,-12,24,-48,\dots$ .

The ratios of consecutive terms are.

  $\frac{-12}{6}=-2,\frac{24}{-12}=-2,\frac{-48}{24}=-2,\dots$

The ratios of consecutive terms for this sequence is constant $-2$ .

Hence, the sequence $\langle s\rangle =6,-12,24,-48,\dots$ is a geometric sequence.

Conclusion:

The sequence $\langle s\rangle =6,-12,24,-48,\dots$ is a geometric sequence.