Chapter SH, Problem 10.4EP

To determine

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

Answer to Problem 10.4EP

The sequence is neither arithmetic nor geometric.

Explanation of Solution

Given:

The given sequence is $2,5,9,12,\mathrm{...}$ .

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.

  $\begin{array}{c}5-2=3\\ 9-5=4\\ 12-9=3\\ ⋮\end{array}$

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

Find the common ratio.

  $\begin{array}{c}\frac{5}{2}=2.5\\ \frac{9}{5}=1.8\\ \frac{12}{9}=\frac{4}{3}\\ ⋮\end{array}$

As, there is no common ratio, so, the sequence is not geometric as well.

Therefore, the sequence is neither arithmetic nor geometric.