Fibonacci Calculator
Generate Fibonacci sequence values up to 100 terms and show the golden-ratio relationship.
Category: Calculators
When to use?
Use it to find the 10th Fibonacci value, inspect the sequence, or study recurrence and golden-ratio patterns.
How to use
- Enter the number of terms n from 1 to 100.
- Review F(1) through F(n).
- Check the nth term and the ratio between neighboring terms.
Input Explanation
Enter an integer from 1 to 100. Larger values are capped to keep the output readable.
Calculation Basis
The sequence starts with F(1)=1 and F(2)=1, then F(n)=F(n-1)+F(n-2). Consecutive-term ratios approach φ = (1+√5)/2.
Usage Examples
- Algorithm learning - Use the sequence as a simple recurrence and dynamic-programming example.
- Pattern study - Inspect how the sequence relates to the golden ratio.
Examples
- F(10) = 55
- Sequence through 10 terms: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55
- F(20) = 6,765, and adjacent-term ratios are already close to the golden ratio
FAQ
Why does the golden ratio appear?
As n grows, F(n+1)/F(n) converges toward φ, approximately 1.618.
Why is the range limited?
Fibonacci numbers grow quickly, so limiting terms keeps browser output and numeric formatting practical.
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