Mathematics · Grades 9–12
Arithmetic sequences
The first term is n = 1. Use one fewer step than the term number.
The key idea
The first term is n = 1. Use one fewer step than the term number.
aₙ = a₁ + (n − 1)d
Worked examples
An arithmetic sequence has first term 17 and common difference 2. Find term 24.
17 + (24 − 1) × 2 = 63
63
An arithmetic sequence has first term 18 and common difference 12. Find term 14.
18 + (14 − 1) × 12 = 174
174
Try it yourself
An arithmetic sequence has first term 12 and common difference 15. Find term 30.
An arithmetic sequence has first term 18 and common difference 4. Find term 25.
Check your understanding
Answers and marking notes
- 447
12 + (30 − 1) × 15 = 447
- 114
18 + (25 − 1) × 4 = 114
Further reading and review references
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Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.