Fibonacci Sequence Generator

Settings

Number of Terms: 10

Generate 1-100 terms

Start From Index: 0

F(0) = 0, F(1) = 1, etc.

Statistics

First term: 0

Last term: 0

Sum: 0

Fibonacci Sequence

Visual Representation

About the Fibonacci Sequence

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones. It starts with 0 and 1, and continues: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89...

Formula

F(n) = F(n-1) + F(n-2)
where F(0) = 0 and F(1) = 1

Applications

Computer algorithms and data structures
Nature: flower petals, pine cones, tree branches
Art and architecture: golden ratio approximation
Financial markets: Fibonacci retracement levels
Music composition and rhythm patterns

Interesting Facts

The ratio between consecutive Fibonacci numbers approaches the golden ratio (φ ≈ 1.618)
Every 3rd number is even, every 4th is divisible by 3
The sequence appears frequently in nature and biological systems
Named after Italian mathematician Leonardo Fibonacci (13th century)