Arithmetic and geometric series · Grade 11
In Grade 11 you learn: arithmetic sequences and series.
A series is the sum of the terms of a sequence. Arithmetic series add the same amount each time; geometric series multiply by the same ratio. Their sum formulas answer questions like “how much will I have saved after five years?” in one step.
Key facts
- Arithmetic: uₙ = a + (n − 1)d and Sₙ = n/2 (2a + (n − 1)d) = n/2 (a + l).
- Sigma notation: Σ uᵣ from r = 1 to n means u₁ + u₂ + … + uₙ.
- a is the first term, d the common difference, r the common ratio and l the last term.