Definition
Common difference
The fixed signed amount added from one term to the next in an arithmetic sequence.
What it means
Picture the jumps between neighboring terms. If every jump changes by the same signed amount, that amount is the common difference. A downward jump gives a negative common difference, and no change gives 0.
Remember it
Same jump, every time—read the jump with its plus or minus sign.
Example
In 31, 26, 21, 16, each term is made by adding −5 to the term before it. The common difference is −5.
Watch for
The sequence 2, 4, 8 has no common difference: its consecutive differences are 2 and 4, not one fixed amount.
Common mix-up
A difference compares one pair. A common difference is the same signed difference for every neighboring pair.
Exact meaning
The common difference is the fixed number added to each term to make the next term in an arithmetic sequence.