Chapter 7.9, Problem 14PPS

To determine

Whether the sequence $4,1,2,\dots$ is an arithmetic, geometric or neither.

Answer to Problem 14PPS

The sequence $4,1,2,\dots$ is neither arithmetic nor geometric.

Explanation of Solution

Given:

The sequence is $4,1,2,\dots$ .

Calculation:

Subtract the first term from the second term of the sequence to obtain the difference.

  $\begin{array}{c}\text{Difference}=1-4\\ =-3\end{array}$

Subtract the second term from the third term of sequence to obtain the difference.

  $\begin{array}{c}\text{Difference}=2-1\\ =1\end{array}$

The difference is not same; therefore, the sequence is not an AP.

Divide the second term by first term of the sequence to obtain the ratio as,

  $\text{Ratio}=\frac{1}{4}$

Divide the third term by second term of the sequence to obtain the ratio as,

  $\text{Ratio}=\frac{2}{1}$

The ratio is not same; therefore, the sequence is not a GP.

Thus, the sequence $4,1,2,\dots$ is neither arithmetic nor geometric.