The idea
Find the common ratio by dividing a term by the preceding non-zero term. Ratios greater than one create growth for positive starting values. A negative ratio makes signs alternate. When r = 1, all terms are equal and the finite sum is simply nu₁. Keep the ratio exact until the final calculation to reduce rounding errors.
Worked example
For 3, 6, 12, 24, … find the fifth term and the sum of the first five terms.
- u₁ = 3 and r = 2.
- u₅ = 3 × 2⁴ = 48.
- S₅ = 3(1 − 2⁵)/(1 − 2) = 93.
A mistake to avoid
A constant difference indicates an arithmetic sequence; a constant ratio indicates a geometric sequence. Check the pattern before choosing a formula.
Check your understanding
What is the fourth term of 16, 8, 4, …?
Show the explanation
The ratio is ½. The fourth term is 16 × (½)³ = 2.
Explore the lesson
This guide connects to Geometric sequences and series in the IB Mathematics: Analysis and Approaches course. The first two published lessons per subject are free previews; further interactive lessons require an account.