Chapter 4.6, Problem 24E

To determine

If the graph represents an arithmetic sequence.

Answer to Problem 24E

It is an arithmetic sequence.

Explanation of Solution

Given information: First four terms of the sequence are pointed on the graph.

Graph:

Arranging the given points in a table in ascending order of $x-axis$ ,

  $\begin{array}{lllll}x\hfill & 1\hfill & 2\hfill & 3\hfill & 4\hfill \\ y\hfill & 5\hfill & 12\hfill & 19\hfill & 26\hfill \end{array}$

In the first pair of coordinates, $x$ increases by $1$ from $1$ to $2$ and y changes by $7$ from $5$ to $12$ .

In the second pair of coordinates, $x$ increases by $1$ from $2$ to $3$ and y changes by $7$ from $12$ to $19$ .

In the third pair of coordinates, $x$ increases by $1$ from $3$ to $4$ and y changes by $7$ from $19$ to $26$ .

As the difference between each pair of consecutive terms is same,

  $\therefore$ it is an arithmetic sequence.