Video Transcript
Use the graph to decide whether the following sequence is an arithmetic sequence.
We will begin by recalling the definition of an arithmetic sequence. A sequence 𝑎 sub 𝑘 is arithmetic if 𝑎 sub 𝑛 plus one minus 𝑎 sub 𝑛 equals 𝑑 for all integers 𝑛. Less formally, we say that a sequence is arithmetic if it has a constant or common difference between each term. In this question, the difference between the first and second term is six, as 11 minus five is six. The difference between the second and third term is also six, which suggests this might be an arithmetic sequence. However, 21 minus 17 is equal to four, so the difference between the third and fourth terms is four. The difference between the fourth and fifth terms is also four. As the difference between each of our terms is not the same, we do not have an arithmetic sequence.
We can also see this directly from the graph. We know that an arithmetic sequence will be represented by a linear graph. Drawing a straight line through the first three points, it is clear that the fourth and fifth points do not lie on this line. We can therefore conclude that the sequence is not an arithmetic sequence.