Chapter 12, Problem 10RE

To determine

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

Answer to Problem 10RE

The given sequence is arithmetic.

Explanation of Solution

Given information:

The sequenceis $0,4,8,12,\mathrm{...}$ .

Calculation:

Consider the sequence.

  $0,4,8,12,\mathrm{...}$

The common difference is,

  $\begin{array}{c}{d}_1=4-0\\ =4\\ d_2=8-4\\ =4\end{array}$

Since, the common difference is equal.

Thus, the sequence is arithmetic.

The sum of terms is,

  $\begin{array}{c}{S}_n=\frac{n}{2}\left[2a_1+\left(n-1\right)d\right]\\ =\frac{n}{2}\left[2\left(0\right)+\left(n-1\right)4\right]\\ =2n\left(n-1\right)\end{array}$