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  • Grade 9
  • Whole terms, nth term

Arithmetic sequence nth term worksheets

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.

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Ready to printArithmetic sequence nth term
Arithmetic sequence nth term worksheet — Whole terms, nth term, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

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.

Why this sheet works

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.

How this one works

One question from this sheet, worked through a step at a time.

3, 2, 1, 0, … — the 23rd term

step = −1
a₂₃=3 + 22 × −1
3 + −22=−19
the 23rd term = −19
  1. This is an arithmetic sequence: it changes by −1 each step (2 − 3 = −1).
  2. The first term is already there, so to reach the 23rd term you take the step only 22 times — that is (n − 1), not n.
  3. 22 steps of −1 is −22, and 3 + −22 = −19.
  4. So the 23rd term is −19.