Chapter 6.5, Problem 16E

To determine

To determine whether the given graph represents an arithmetic sequence or a geometric sequence or neither .

Answer to Problem 16E

The given sequence is neither a arithmetic sequence nor a geometric sequence.

Explanation of Solution

Given information:

Given graph

  

The sequence obtained from given graph is $4,11,16,19$ is not arithmetic sequence because there does not exists any common difference

  $\begin{array}{l}d=a_2-a_1=11-4=7and\text{also}{a}_3-a_2=16-11=5\\ \Rightarrow 7\ne 5\end{array}$

Similar way the given sequence is not a geometric sequence as well because there does not any common ratio

  $\begin{array}{l}r=\frac{a_2}{a_1}=\frac{11}{4}andalso\frac{a_3}{a_2}=\frac{16}{11}\\ \Rightarrow \therefore \frac{11}{4}\ne \frac{16}{11}\end{array}$

Hence, the given sequence is neither a arithmetic sequence nor a geometric sequence.