Common difference of a sequence worksheets

The common difference is the step an arithmetic sequence takes every time, and finding it is where every other sequence question begins. These free printable worksheets practice that one move — subtract two neighboring terms — and nothing else.

Common difference of a sequence
Common difference of a sequence worksheet — Whole common differences, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

For 5, 12, 19, 26 the difference is 12 − 5 = 7, and the same 7 shows up between every other pair, which is what makes the sequence arithmetic in the first place. Doing the subtraction at two different points and checking they agree is the built-in test that the rule is real, and these sheets are short on purpose so a child can do that check every time.

Why this sheet works

The direction of the subtraction matters. A falling sequence like 20, 17, 14, 11 has a common difference of −3, not 3, and a child who subtracts the smaller from the larger loses the sign that tells the sequence which way it goes. Every step-by-step walk here subtracts later term minus earlier term, so a decreasing sequence reports a negative difference.

How this one works

−9, −5, −1, 3, 7, … — the common difference

−5 − −9=4
d = 4
  1. Each term is the one before it plus the same number. Subtract any term from the next: −5 − −9 = 4.
  2. Check it holds all the way along, then that number is the common difference: 4.