Question

What is an arithmetic sequence?

Answer 1

An arithmetic sequence is a sequence (list of numbers) that has a common difference (a positive or negative constant) between the consecutive terms.

Here are some examples of arithmetic sequences:
1.)7, 14, 21, 28 because Common difference is 7.
2.) 48, 45, 42, 39 because it has a common difference of - 3.

The following are not examples of arithmetic sequences:

1.) 2,4,8,16 is not because the difference between first and second term is 2, but the difference between second and third term is 4, and the difference between third and fourth term is 8. No common difference so it is not an arithmetic sequence.

2.) 1, 4, 9, 16 is not because difference between first and second is 3, difference between second and third is 5, difference between third and fourth is 7. No common difference so it is not an arithmetic sequence.

3.) 2, 5, 7, 12 in not because difference between first and second is 3, difference between second and third is 2, difference between third and fourth is 5. No common difference so it is not an arithmetic sequence.