Arithmetic and geometric sequencesThe nth term of an arithmetic sequence
Find the term shown for each sequence.
The nth term of an arithmetic sequence is a jump, not a walk: instead of counting term by term you add the common difference (n − 1) times to the start. These free printable worksheets ask for one term too far out to reach by hand.
Kid stuck on one? You don’t just get the sheet.

The answer key prints on a separate page.
The formula is a₁ + (n − 1)d, and it earns its keep the moment the question asks for the 20th term. For 5, 12, 19, … the common difference is 7, so the 20th term is 5 + 19 × 7 = 138 — found in one line rather than by writing out nineteen more numbers. Where the combined sequences sheet mixes this with finding the rule and with geometric terms, this page holds to arithmetic terms alone so the (n − 1) count becomes second nature.
The single most common slip is using n instead of (n − 1): the first term is already sitting there, so the step is taken one fewer time than the term number. A child who adds d twenty times overshoots by exactly one step, and every step-by-step walk here writes the (n − 1) out before it multiplies.
One question from this sheet, worked through a step at a time.
3, 2, 1, 0, … — the 23rd term