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
- This is an arithmetic sequence: it changes by 1 each step (−8 − −9 = 1).
- 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.
- 23 steps of 1 is 23, and −9 + 23 = 14.
- So the 24th term is 14.
How it works.
- 01
This is an arithmetic sequence: it changes by 1 each step (−8 − −9 = 1).
- 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.
- 03
23 steps of 1 is 23, and −9 + 23 = 14.
- 04
So the 24th term is 14.