Exercise 23 Page 204

There are two ways for us to determine whether the given graph represents an arithmetic sequence.

1. Graphically. Check if all the points lie on the same straight line.
2. Numerically. Observe if the difference between consecutive terms in the sequence is constant.

We will determine if the graph represents an arithmetic sequence by using these two methods.

Graphically

Using a straight edge, we will try to draw a line that passes through all the points.

The four points do not line on the same line. Therefore, the graph does not represent an arithmetic sequence.

Numerically

To observe the difference between consecutive terms in the sequence, let's first organize the ordered pairs in a table.

Position, $n$	$1$	$2$	$3$	$4$
Term, $a_n$	$1$	$4$	$1$	$4$

Let's now calculate the difference between consecutive terms. There is no common difference between these terms. We can therefore conclude that the sequence is not an arithmetic sequence.