What is the Fibonacci sequence?

F(0)=0, F(1)=1, F(n)=F(n-1)+F(n-2). Sequence: 0,1,1,2,3,5,8,13,21,34,55,89,144... Each term is the sum of the two before it. Found extensively in nature: sunflower spirals, shell growth, tree branching.

What is the golden ratio?

The golden ratio φ ≈ 1.6180339887... As Fibonacci numbers get larger, the ratio of consecutive terms converges to φ. φ=(1+√5)/2. Appears in art, architecture, and design. F(n+1)/F(n) → φ as n→∞.

What is the Fibonacci sequence?

F(0)=0, F(1)=1, F(n)=F(n-1)+F(n-2). Sequence: 0,1,1,2,3,5,8,13,21,34,55,89,144... Each term is the sum of the two before it. Found extensively in nature: sunflower spirals, shell growth, tree branching.

What is the golden ratio?

The golden ratio φ ≈ 1.6180339887... As Fibonacci numbers get larger, the ratio of consecutive terms converges to φ. φ=(1+√5)/2. Appears in art, architecture, and design. F(n+1)/F(n) → φ as n→∞.

Fibonacci Sequence Generator — First N Terms

Free Fibonacci sequence generator. Generate the first N terms of the Fibonacci sequence. Find any specific Fibonacci number. View the golden ratio and interesting Fibonacci facts.

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