Science & Math Math calculation

Arithmetic Sequence Solver

Find nth term and sum of an arithmetic progression from a, d, and n.

Arithmetic Sequence Solver calculates the nth term and partial sum from the first term, common difference, and term count. Use it to check sequence homework, spreadsheet formulas, or planning models where each step changes by a fixed amount.

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Input guidance

Enter the first term.

How to use this tool

Enter the first term.
Enter the common difference between consecutive terms.
Enter n and review the nth term plus the partial sum for the first n terms.

Sequence Inputs

For arithmetic progression: a, d, n.

Results

Nth term: 21.000000

Sum of first n terms: 120.000000

Preview terms: 3.0, 5.0, 7.0, 9.0, 11.0, 13.0, 15.0, 17.0, 19.0, 21.0

Formula or method

n is clamped from 1 to 10000.
The nth term is first_term + (n - 1) * common_difference.
The partial sum is n/2 * (2*first_term + (n - 1)*common_difference).
Preview terms are generated with the same arithmetic progression for up to the first 20 terms.

How to interpret the result

Check units, model assumptions, rounding, and whether the formula matches the scenario before relying on the result.

Confidence and limitations

Outputs are deterministic formula results and depend entirely on input quality and units.
Results are for planning and learning; verify with domain standards before safety-critical use.
Rounding and finite precision can introduce small differences in edge cases.

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