Chapter 6.5, Problem 17E

To determine

To find: whether thegraph represents an arithmetic sequence or the geometric sequence or neither.

Answer to Problem 17E

Neither

Explanation of Solution

Given information:

The graph:

  

Concept Used:

In Arithmetic sequence difference between each pair of consecutive terms is same.

In Geometric sequence the ratio between each pair of consecutive terms is same.

First find the difference between each pair of consecutive terms:

  $\begin{array}{c}60-120=-60\\ 20-60=-40\\ 5-20=-15\end{array}$

Now, find the ratio between each pair of consecutive terms:

  $\begin{array}{c}\frac{60}{120}=\frac{1}{2}\\ \frac{20}{60}=\frac{1}{3}\\ \frac{5}{20}=\frac{1}{4}\end{array}$

There is neither a common difference nor a common ratio between the terms.

So, the graph represents neither an arithmetic sequence nor a geometric sequence.