We can determine if a graphed sequence is arithmetic both graphically and numerically.
No
Practice makes perfect
There are two ways for us to determine if the given graph represents an arithmetic sequence.
Graphically: Check to see if all of the points lie on the same straight line.
Numerically: Observe if the difference between each term in the sequence is constant.
Graphically
Using a straightedge, we will try to draw a line that passes through all of the points.
There is no one straight line on which all of the points lie. Therefore, the graph does not represent an arithmetic sequence.
Numerically
To observe the difference between each term in the sequence, let's first organize the given ordered pairs in a table of values.
n
a_n
1
2
2
4
3
7
4
11
To determine if the difference between one term and the next is constant, let's compare the change between a_n terms.
2+2 →4+3 →7+4 →11
There is no common difference between these terms. We can therefore conclude that the sequence is not arithmetic.
