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Formula verified · Deterministic calculation

Sequence Calculator

Find the nth term, finite sum and initial terms of an arithmetic progression from its first term and common difference.

Nth term19
Sum of first n terms
100
Term preview
1, 3, 5, 7, 9, 11, 13, 15, 17, 19

Trend

59
611
713
815
917
1019
Methodology

The certified arithmetic-sequence engine calculates the nth term and finite sum, while the Free trend preview is generated from the same progression.

Sources
  • CalcuMint deterministic sequence engine
Solution steps
  1. aₙ = 1 + (10-1)×2 = 19
  2. Sₙ = 10(1+19)/2 = 100

How this calculator works

For an arithmetic sequence, aₙ=a₁+(n−1)d and Sₙ=n(a₁+aₙ)/2.

Formula

aₙ=a₁+(n-1)d; Sₙ=n(a₁+aₙ)/2

Computes an arithmetic sequence term and finite sum.

Worked example

First 10 odd numbers is a verified test case used by the calculation engine.

Assumptions and limitations

  • This certified version covers arithmetic sequences.
  • n is an integer from 1 through 1000; the preview shows at most 20 terms.

Methodology & sources

This calculator uses deterministic, versioned calculation logic. The formula and verified examples above are part of the calculation definition used by CalcuMint. Technical calculation version: 1.

  • CalcuMint deterministic sequence engine — Standard arithmetic progression identities.

Frequently asked questions

Which sequence type is supported?

This version calculates arithmetic sequences with a constant common difference.

Does it calculate the sum?

Yes. It returns the nth term and the sum of the first n terms.

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Sequence Calculator | CalcuMint