How to Use the Fibonacci Sequence Generator
Enter n to instantly compute the nth Fibonacci number starting from F(1)=1, F(2)=1 (standard convention). Each term is the sum of the two preceding ones: F(n) = F(nβ1) + F(nβ2). The tool uses JavaScript BigInt for precise calculations up to F(200).
Key Properties of the Fibonacci Sequence
- F(1)=1, F(2)=1, F(3)=2, F(4)=3, F(5)=5, F(6)=8, ...
- The ratio F(n+1)/F(n) converges to the golden ratio Ο β 1.618
- Appears in natural spirals: snail shells, sunflower seeds, pine cones
- Classic example for dynamic programming in algorithm courses
Frequently Asked Questions
What is the golden ratio connection?
As n grows, the ratio of consecutive Fibonacci terms approaches Ο β 1.6180339... This is why Fibonacci spirals appear throughout nature and art.
Are there any Fibonacci prime numbers?
Yes β Fibonacci primes include F(3)=2, F(4)=3, F(5)=5, F(7)=13, F(11)=89. Whether infinitely many exist remains an open mathematical question.
Is F(200) accurate without rounding?
Yes. BigInt avoids floating-point precision loss, so even F(200) β a 42-digit number β is computed exactly.