Concept 5 of 19Foundation
Watch on YouTubeVideoFibonacci — nature's own sequence
The Fibonacci sequence starts with two 1's. Each next term is the sum of the previous two.
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, …
Rule: Fₙ = Fₙ₋₁ + Fₙ₋₂, with F₁ = F₂ = 1.
It appears everywhere in nature: petal counts (3, 5, 8, 13, 21), spirals in sunflowers and pinecones, arrangement of leaves on stems (phyllotaxis). The ratio Fₙ₊₁/Fₙ approaches the Golden Ratio (≈ 1.618) — used in art and architecture.
Example
F₇ = F₆ + F₅ = 8 + 5 = 13.
F₁₀ = 55. F₁₂ = 144 (also a square!).
F₁₀ = 55. F₁₂ = 144 (also a square!).
💡 Tip:Fibonacci is a recursive pattern — different from arithmetic (fixed add) and geometric (fixed multiply).
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5 questions to check what you just read.
0 / 5
- Q1.F₈ in 1, 1, 2, 3, 5, 8, 13, …?
- Q2.Missing term: 1, 1, __, 3, 5, 8?
- Q3.Next: 5, 8, 13, 21, 34, ?
- Q4.Is 34 a Fibonacci number?
- Q5.Sum F₁ + F₂ + F₃ + F₄ + F₅ in 1, 1, 2, 3, 5?