Finite Difference Sequence Calculator
Build an exact integer difference table and extrapolate an equally spaced sequence under its interpolating-polynomial model.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Construct successive exact differences, extend the deepest constant row and add back upward for each next polynomial-model value.
Δaᵢ=aᵢ₊₁−aᵢ; extend constant highest difference and reconstruct upward
Worked example
1, 4, 9, 16 has first differences 3, 5, 7 and constant second difference 2. Its degree-two polynomial model gives next values 25, 36 and 49.
Assumptions and input details
Integers have up to 50 digits each and use exact arithmetic. Index spacing is assumed equal. Every finite prefix has a polynomial interpolation, so exact extrapolation does not establish the real generating rule. The displayed degree is the least interpolating degree identifiable under exact equal-step data, not a prediction guarantee. No external sequence database or pattern guessing is used.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Integer values and finite-difference extrapolations use exact BigInt arithmetic. Future values assume a polynomial sequence of the inferred finite degree; the data alone do not prove that continuation.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
Find the nth term and sum of an arithmetic or geometric sequence. Inspect terms, running totals, a term graph and a convergent geometric sum where applicable.
Differentiate a polynomial of degree up to six, evaluate its slope at a point and find the tangent line. Enter coefficients and follow each power-rule term.
Enter two known points and a target x or y. Calculate the other coordinate, view the straight-line model and clearly distinguish interpolation from extrapolation.
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