Chapter 4.7, Problem 56PPE

To determine

whether the sequence $1,8,27,64,\mathrm{......}$ is arithmetic and if it is ,then find recursive formula and explicit formula for it.

Answer to Problem 56PPE

The sequence is not an arithmetic sequence.

Explanation of Solution

Given sequence: $1,8,27,64,\mathrm{......}$

Calculation:

If each term of given sequence after the first term is obtained by adding the previous one by a fixed constant, then the sequence is an arithmetic sequence and the fixed constant is common difference.

The difference of the terms with the previous term is

  $\begin{array}{l}8-1=7\\ 27-8=19\\ 64-27=37\end{array}$

Since difference between two consecutive terms is not fixed.

Therefore, the sequence is not arithmetic