Tell whether the sequence is arithmetic. If it​ is, identify the common difference.

Question

negative 3
​,
5
​,
13
​,
21
​,
...
Question content area bottom
Part 1
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The sequence is arithmetic and has a common difference of enter your response here
.
B.
The sequence is not arithmetic.

Answer 1

An arithmetic sequence is a sequence of numbers in which the difference of any two successive members is a constant. This difference is known as the common difference.

Let's check if the given sequence is arithmetic by finding the differences between successive terms:

The sequence is: -3, 5, 13, 21, ...

First difference:
5 - (-3) = 5 + 3 = 8

Second difference:
13 - 5 = 8

Third difference:
21 - 13 = 8

Since the differences between each pair of successive terms are all the same (8), the sequence is arithmetic.

So the correct choice is:

A. The sequence is arithmetic and has a common difference of 8.