Question

Which of the following is true regarding the sequence graphed below?

Answer 1

Answer:  The correct option is

(D) The sequence is not arithmetic because the terms do not have a common difference.

Step-by-step explanation:  We are given to select the true statement regarding the sequence that is graphed in the figure.

From the graph, we see that some of the points are (1, 1), (2, 4), (3, 9), (4, 16), (5, 25).

That is, if we write the graphed points in terms of a sequence <a(n)>, then we get

$a(1)=1,\\\\a(2)=4,\\\\a(3)=9,\\\\a(4)=16,\\\\a(5)=25.$

The sequence <a(n)> will be arithmetic if the difference between the consecutive terms is equal. That is, the terms should have a common difference.

Now,

$a(2)-a(1)=4-1=3,\\\\a(3)-a(2)=9-4=6,\\\\a(4)-a(3)=16-9=7,\\\\a(5)-a(4)=25-16=9.$

This implies that the terms do not have a common difference and so the graphed function does not represent an arithmetic sequence.

Thus, the sequence is not arithmetic because the terms do not have a common difference.

Option (D) is CORRECT.