Question 1

What is the Fibonacci sequence?

Accepted Answer

F(0)=0, F(1)=1, F(n)=F(n−1)+F(n−2). Each number is the sum of the previous two: 0,1,1,2,3,5,8,13,21,34,55...

Question 2

What is the golden ratio?

Accepted Answer

φ = (1+√5)/2 ≈ 1.6180339887. As n→∞, F(n)/F(n−1) → φ. The golden ratio appears in art, architecture, and nature (spirals, branching).

Question 3

What is F(10)?

Accepted Answer

F(10) = 55. The sequence: 0,1,1,2,3,5,8,13,21,34,55.

Question 4

Is there a formula for the nth Fibonacci number?

Accepted Answer

Yes — Binet's formula: F(n) = (φⁿ − ψⁿ)/√5, where φ=(1+√5)/2 and ψ=(1−√5)/2. For large n, the ψⁿ term is tiny so F(n) ≈ φⁿ/√5.

Question 5

Where does Fibonacci appear in nature?

Accepted Answer

Flower petals (usually Fibonacci numbers), sunflower seed spirals, pine cone scales, nautilus shell proportions, and tree branch patterns.

Fibonacci Calculator — nth Term & Sequence

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