Fibonacci Sequence Generator
Everyday
The Fibonacci sequence starts with 0 and 1, and each following number is the sum of the two before it: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on. Enter how many terms you want and this tool lists them all, reports the last term, the sum of every term in the list, and the ratio of the final two terms, which converges toward the golden ratio φ ≈ 1.618034. Every value is computed with arbitrary-precision big integers, so even the hundredth or thousandth term is exact rather than rounded. Everything runs locally in your browser — nothing is uploaded.
How to use
- Enter the number of terms you want to generate (1 to 1000).
- Read the last (Nth) term, the sum of all listed terms and the golden-ratio approximation.
- Scroll the full sequence and copy it with one click.
- Try 10 terms (0, 1, 1, 2, 3, 5, 8, 13, 21, 34 — sum 88) to check the output.
Frequently asked questions
- Where does the sequence start?
- This generator uses the standard convention F(0) = 0, F(1) = 1, so the first ten terms are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34. The 'last term' stat is the final number in the list you generated.
- Are large terms exact?
- Yes. Calculations use JavaScript big integers, so terms with hundreds of digits are computed exactly with no floating-point rounding. For example F(100) — which appears as the 101st value because the list starts at F(0) — is exactly 354224848179261915075.
- What is the golden-ratio number?
- It is the ratio of the last term to the one before it. As the sequence grows this ratio converges to the golden ratio φ ≈ 1.6180339887, which is why Fibonacci numbers and φ are so closely linked.
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