Concept 3 of 19Foundation
Watch on YouTubeVideoGeometric sequences (multiply the same)
A geometric sequence multiplies (or divides) by the same number each step — the common ratio (r).
- 2, 4, 8, 16, 32… (r = 2 — doubling)
- 1, 3, 9, 27, 81… (r = 3 — powers of 3)
- 100, 50, 25, 12.5… (r = ½ — halving)
nth-term formula: aₙ = a · rⁿ⁻¹
Doubling explodes fast: 1 doubles 20 times reaches 1,048,576!
Example
A rumour doubles every round. Round 1: 2 people. After 5 rounds: 2·2⁵⁻¹ = 32 people.
💡 Tip:Same ratio between neighbours? It's geometric.
▸Why does this work? (derivation)
Why aₙ = a · rⁿ⁻¹? Start at a. After 1 multiplication: a·r. After 2: a·r². After (n−1) multiplications: a·rⁿ⁻¹.
🎯 Try it!
5 questions to check what you just read.
0 / 5
- Q1.Common ratio of 2, 10, 50, 250?
- Q2.Next term of 4, 12, 36, 108, …?
- Q3.Which is geometric?
- Q4.6th term of 3, 6, 12, 24, …?
- Q5.Next in 160, 80, 40, 20, …?