Algebra 2 · Unit 9 · Topic 9.3
Finite Geometric Series
A geometric sequence has constant ratio r.
Definition and explanation
A geometric sequence has constant ratio r. For r ≠ 1, the first n terms sum to Sₙ = a₁(1 − rⁿ)/(1 − r); when r = 1, the sum is na₁.
Worked example
Sum 3 + 6 + 12 + 24 + 48. With a₁ = 3, r = 2, and n = 5, S₅ = 3(1 − 2⁵)/(1 − 2) = 93. Direct addition confirms 93.
Common mistake
The exponent n counts terms, while the last term uses r^(n − 1).
Key takeaway
A geometric sequence has constant ratio r.
Explain each step of the worked example, then check the units, signs, and conditions that apply.
Further reading
Topic coverage was checked against the openly available OpenStax Intermediate Algebra 2e, Algebra and Trigonometry 2e, and Introductory Statistics 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.