Sequences & Series
Arithmetic sequences add a constant. Geometric sequences multiply by a constant.
The rules
- Arithmetic: aₙ = a₁ + (n − 1)d. Geometric: aₙ = a₁ · rⁿ⁻¹.
- Sum of an arithmetic series = n(a₁ + aₙ) / 2.
- Infinite geometric series with |r| < 1: S = a₁ / (1 − r).
- Find the common difference or ratio first.
Watch out: Using n instead of n − 1 in the formula.
Worked example
What is the sum of 1 + 2 + 3 + … + 20?
- Use n(a₁ + aₙ)/2.
- 20(1 + 20)/2 = 210.
Answer: 210
Try it yourself
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