Fibonacci Generator

Generate Fibonacci sequence numbers

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Number of Terms

Starting Index

Fibonacci Sequence

F₀ = 0 F₁ = 1 F₂ = 1 F₃ = 2 F₄ = 3 F₅ = 5 F₆ = 8 F₇ = 13 F₈ = 21 F₉ = 34 F₁₀ = 55 F₁₁ = 89 F₁₂ = 144 F₁₃ = 233 F₁₄ = 377

Find Nth Fibonacci Number

=55

Golden Ratio (φ)

φ = (1 + √5) / 21.61803398871/φ = φ - 10.6180339888φ² = φ + 12.6180339886

Ratio Convergence to φ

F₂/F₁:1.0000000000

F₃/F₂:2.0000000000

F₄/F₃:1.5000000000

F₅/F₄:1.6666666667

F₆/F₅:1.6000000000

F₇/F₆:1.6250000000

F₈/F₇:1.6153846154

F₉/F₈:1.6190476190

F₁₀/F₉:1.6176470588

F₁₁/F₁₀:1.6181818182

F₁₂/F₁₁:1.6179775281

F₁₃/F₁₂:1.6180555556

F₁₄/F₁₃:1.6180257511

F₁₅/F₁₄:1.6180371353

Properties of F₁₀

Digit count:2Is prime:NoBinet formula:(φ^n - ψ^n) / √5

Check if Number is Fibonacci

Fibonacci Facts

• Every 3rd Fibonacci number is divisible by 2

• Every 4th Fibonacci number is divisible by 3

• Every 5th Fibonacci number is divisible by 5

• The sum of first n Fibonacci numbers = F(n+2) - 1

• F(n-1) × F(n+1) - F(n)² = (-1)^n (Cassini's identity)

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