Chapter 7.9, Problem 2CYU

To determine

Whether the sequence $2,4,16,\dots$ is an arithmetic, geometric or neither.

Answer to Problem 2CYU

The sequence $2,4,16,\dots$ is neither arithmetic nor geometric.

Explanation of Solution

Given:

The sequence is $2,4,16,\dots$ .

Calculation:

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

  $\begin{array}{c}\text{Difference}=4-2\\ =2\end{array}$

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

  $\begin{array}{c}\text{Difference}=16-4\\ =12\end{array}$

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,

  $\begin{array}{c}\text{Ratio}=\frac{4}{2}\\ =2\end{array}$

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

  $\begin{array}{c}\text{Ratio}=\frac{16}{4}\\ =4\end{array}$

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

Thus, the sequence $2,4,16,\dots$ is neither arithmetic nor geometric.