Arithmetic sequence nth term, step by step

The nth term of an arithmetic sequence is a jump, not a walk.

The question

−9, −8, −7, −6, … — the 24th term

d = 1
aₙ = −9 + (n − 1) × 1
a₂₄=−9 + 23 × 1
−9 + 23=14
a₂₄ = 14
  1. This is an arithmetic sequence: it changes by 1 each step (−8 − −9 = 1).
  2. The first term is already there, so to reach the 24th term you take the step only 23 times — that is (n − 1), not n.
  3. 23 steps of 1 is 23, and −9 + 23 = 14.
  4. So the 24th term is 14.

How it works.

  1. 01

    This is an arithmetic sequence: it changes by 1 each step (−8 − −9 = 1).

  2. 02

    The first term is already there, so to reach the 24th term you take the step only 23 times — that is (n − 1), not n.

  3. 03

    23 steps of 1 is 23, and −9 + 23 = 14.

  4. 04

    So the 24th term is 14.