Math
Geometric sequences.
Definition
A sequence of numbers where each term is found by multiplying the previous term by a fixed number called the common ratio (r). The sequence grows or shrinks by the same factor each step.
Examples
Real-world.
- 1 2, 6, 18, 54, ... has common ratio r = 3
- 2 100, 50, 25, 12.5, ... has common ratio r = 0.5
- 3 A bank account doubling yearly: $500, $1000, $2000, $4000
Key Fact
aₙ = a₁ · r^(n−1), sum of n terms: Sₙ = a₁(1 − rⁿ)/(1 − r)