Quadratic Sequence Calculator
Enter consecutive terms starting at n = 1. A formula is shown only when every supplied term matches the fitted model within the stated tolerance.
A QUICK WALKTHROUGH
How to use this tool
- Enter 4–20 numbers separated by commas or whitespace.
- Enter an integer target position n ≥ 1.
- Fit the first three terms, check all terms, and review the conditional result.
Model and indexing
Positions are consecutive integers beginning at 1. Let d = x₂ − x₁ and s = x₃ − 2x₂ + x₁. The model is aₙ = x₁ + (n − 1)d + (n − 1)(n − 2)s/2. In aₙ = An² + Bn + C, A = s/2, B = d − 3A, C = x₁ − A − B. Zero second difference permits linear or constant models.
Tolerance and limits
Every supplied value x is checked against prediction p with |x − p| ≤ 10⁻⁹ + 10⁻⁹ max(|x|, |p|). Numbers use browser floating point; inputs, intermediate calculations and results must be finite and no larger in magnitude than 9,007,199,254,740,991. The target must be a safe integer. No formula is given for a mismatch.
Interpretation and privacy
Finite samples can fit many different continuations. Matching this degree-at-most-two model does not establish a unique infinite sequence. The target value assumes this model continues. Calculations stay in your browser.
GOOD TO KNOW
Common questions
Does a match prove the pattern?
No. It only checks the supplied terms under this particular model and tolerance.