Chapter 12, Problem 8RE

To determine

To find:Whether given sequence is arithmetic, geometric or neither.

Answer to Problem 8RE

The given sequence is arithmeticisneither.

Explanation of Solution

Given information:

The sequenceis $c_n=2n^3$ .

Calculation:

Consider the sequence.

  $c_n=2n^3$

The terms of sequence are,

  $\begin{array}{l}{c}_1=2\\ c_2=16\\ c_3=54\\ c_4=128\end{array}$

The common difference is,

  $\begin{array}{c}{d}_1=16-2\\ =14\\ d_2=54-16\\ =38\end{array}$

The common ratio is,

  $\begin{array}{c}{r}_1=\frac{16}{2}\\ =8\\ r_2=\frac{54}{16}\\ =\frac{27}{8}\end{array}$

Since, neither common difference nor ratio is equal.

Thus, the sequence is neither.