Geometric sequences

Math

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

  • 2, 6, 18, 54, ... has common ratio r = 3
  • 100, 50, 25, 12.5, ... has common ratio r = 0.5
  • 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)

Related Terms

Arithmetic sequences Exponential growth and decay Sigma notation

Study This Concept

Practice geometric sequences with free review games in these units:

Algebra 2 Unit 8: Sequences and Series