An arithmetic sequence has first term a and common difference d. Its nth term is uₙ = a + (n − 1)d. For 11, 14, 17, …, u₁₃ = 11 + 12 × 3 = 47.
The sum of the first n terms is Sₙ = n/2 × (2a + (n − 1)d). This comes from writing the series forwards and backwards and adding the pairs. For 2, 7, 12, …, S₂₆ = 13 × (4 + 25 × 5) = 1677.
Worked example
Find S₁₀ for 5, 8, 11, …
- a = 5, d = 3, n = 10.
- S₁₀ = 5 × (10 + 9 × 3) = 5 × 37.
Answer:185
Key words
- series
- the sum of the terms of a sequence
- common difference (d)
- the amount added each time
- Sₙ
- the sum of the first n terms
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Common Core-referenced: HSF-BF.A.2