Definition
Arithmetic sequence
A number sequence made by adding the same signed amount at every step.
What it means
Walk through the sequence using one repeatable add step. Subtracting 4 is the same as adding −4, so an arithmetic sequence can rise, fall, or stay level.
Remember it
Arithmetic sequence: repeat one add step.
Example
12, 17, 22, 27 is arithmetic because each term is 5 more than the one before it. Its common difference is 5, so the next term is 32.
Watch for
1, 2, 4, 7 is not arithmetic: the added amounts are 1, 2, and 3 rather than one fixed amount.
Common mix-up
Arithmetic sequences repeat an additive step; geometric sequences repeat a multiplicative step.
Exact meaning
An arithmetic sequence is a number sequence in which one fixed amount is added to each term to make the next term.