Chapter SH, Problem 10.2EP

To determine

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

Answer to Problem 10.2EP

The sequence is geometric.

Explanation of Solution

Given:

The given sequence is $4,12,36,108,\mathrm{...}$ .

Calculation:

In an arithmetic sequence, each term is determined by adding a constant value to the previous term. This constant value is called the common difference.

In the geometric sequence, check for the common ratio.

Find the common difference as follows.

  $\begin{array}{c}12-4=8\\ 36-12=24\\ 108-36=72\\ ⋮\end{array}$

As, there is no common difference, so, the sequence is not arithmetic.

Find the common ratio.

  $\begin{array}{c}\frac{12}{4}=3\\ \frac{36}{12}=3\\ \frac{108}{36}=3\\ ⋮\end{array}$

Therefore, the common ratio is $3$ so the sequence is geometric.