To graphically determine whether the graph represents an arithmetic sequence check if the points lie on the same line.
Does the Graph Represent an Arithmetic Sequence? Yes. Explanation: Consecutive terms have a common difference of 7.
Practice makes perfect
There are two ways for us to determine whether the given graph represents an arithmetic sequence.
Graphically. Check if all the points lie on the same straight line.
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.
We see that all the points lie on the same line. Therefore, the graph represents 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
5
12
19
26
Let's now calculate the difference between consecutive terms.
5+ 7 ⟶12+ 7 ⟶19+ 7 ⟶26
Here we see that the difference between consecutive terms is constant and equal to 7. Therefore, the sequence is an arithmetic sequence with a common difference of 7.
