Chapter 7.8, Problem 11PPE

To determine

Todetermine:whether the given sequence is a geometric sequence.

Answer to Problem 11PPE

The sequence $\langle s\rangle =5,10,15,20,\dots$ is not a geometric sequence.

Explanation of Solution

Given information:

The given sequence is $5,10,15,20,\dots$ ,

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 $\langle s\rangle =5,10,15,20,\dots$ , that may be written as

  $\langle s\rangle =5,5\times 2,5\times 3,5\times 4,\dots$ .

The ratios of consecutive terms for this sequence is not constant, it is $\frac{5\times 2}{5}=2,\frac{5\times 3}{5\times 2}=\frac{3}{2},\frac{5\times 4}{5\times 3}=\frac{4}{3},\dots$

Hence, the sequence $\langle s\rangle =5,10,15,20,\dots$ is not a geometric sequence.

Conclusion:

The sequence $\langle s\rangle =5,10,15,20,\dots$ is not a geometric sequence.