Fibonacci Sequence Generator
Number of terms (1–50)
The Fibonacci sequence starts with 0 and 1, and each subsequent number is the sum of the two preceding ones. It appears throughout nature — in flower petals, spiral shells, and the golden ratio.
- 1F(0)=0, F(1)=1
- 2F(n) = F(n−1) + F(n−2)
- 3Ratio of consecutive terms approaches φ = 1.618... (golden ratio)
- 4Formula: F(n) = (φⁿ − ψⁿ)/√5 (Binet's formula)
First 10 terms=0, 1, 1, 2, 3, 5, 8, 13, 21, 34
F(20)=6765
| n | F(n) | Ratio F(n)/F(n-1) |
|---|---|---|
| 5 | 5 | 1.667 |
| 10 | 55 | 1.618 |
| 15 | 610 | 1.618 |
| 20 | 6765 | 1.618 |
| 25 | 75025 | 1.618 |
References
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