Chapter 4.6, Problem 25E

To determine

If the graph represents an arithmetic sequence.

Answer to Problem 25E

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 $x-axis$ ,

  $\begin{array}{lllll}x\hfill & 1\hfill & 2\hfill & 3\hfill & 4\hfill \\ y\hfill & 70\hfill & 55\hfill & 40\hfill & 25\hfill \end{array}$

In the first pair of coordinates, $x$ increases by $1$ from $1$ to $2$ and y changes by $-15$ from $70$ to $55$ .

In the second pair of coordinates, $x$ increases by $1$ from $2$ to $3$ and y changes by $-15$ from $55$ to $40$ .

In the third pair of coordinates, $x$ increases by $1$ from $3$ to $4$ and y changes by $-15$ from $40$ to $25$ .

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

  $\therefore$ it is an arithmetic sequence.