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Arithmetic Series Sum from First Term, Last Term, and Count Calculator

S_n = n · (a₁ + aₙ) / 2.

Compute the sum of an arithmetic series: S_n = n(a₁ + aₙ)/2, where a₁ is the first term, aₙ the last, and n the count of terms. Also computes the common difference d = (aₙ − a₁)/(n − 1) and reports the mean (average) of the series.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

S_n = n·(a₁ + aₙ)/2; d = (aₙ−a₁)/(n−1).

In depth

Compute the sum of an arithmetic series: S_n = n(a₁ + aₙ)/2, where a₁ is the first term, aₙ the last, and n the count of terms. Also computes the common difference d = (aₙ − a₁)/(n − 1) and reports the mean (average) of the series.