Arithmetic Series Calculator
The Arithmetic Series Calculator adds the terms of an arithmetic series using its first term, last term, and number of terms.
What this calculator does
The Arithmetic Series Calculator estimates your result instantly from the values you enter, using standard math & conversions formulas. The Arithmetic Series Calculator adds the terms of an arithmetic series using its first term, last term, and number of terms. Calculations run in your browser, so nothing you type is sent to a server, and the output is an estimate rather than a certified or official figure.
Result
About Arithmetic Series Calculator
An arithmetic series is the sum of the terms of an arithmetic sequence. When you know the first term a1, the last term an, and the number of terms n, the sum is Sn = (n ÷ 2) × (a1 + an).
Enter those three values and the calculator returns the sum of the series.
Formula & Mathematical Calculation
sumN = (n ÷ 2) × (a1 + an)
Derived directly from the verified calculation function in the tool engine.
Calculation Example
For a first term of 2, a last term of 50, and 25 terms, the sum is (25 ÷ 2) × (2 + 50) = 12.5 × 52 = 650.
Key Benefits
- Sums a series directly from the first term, last term, and term count
- Uses the closed-form formula, so no manual term-by-term addition
- Accepts negative and decimal values
- Runs in your browser with no data sent to a server
How to Use this Calculator
-
Enter the first term
Type the first term of the series into the a1 field. -
Enter the last term
Type the final term into the an field. -
Enter the number of terms
Type how many terms the series has, as a whole number of at least 1. -
Calculate
Press Calculate to see the sum of the series.
Assumptions & Limitations
What the calculation assumes
- Every value you enter is treated as an exact, known amount.
- Any rate or interval you enter is assumed to hold for the whole period unless the form asks for it separately.
- Results use standard published formulas and account only for the values entered above.
- Rounding is applied for display; the underlying calculation uses your full precision.
- Results are returned in the same units you enter, unless the tool states the output unit.
What it does not cover
- Arithmetic Series Calculator produces a calculated result for reference and learning, not a certified or official measurement.
- Real-world outcomes differ when tolerances, rounding rules or local standards apply.
- Definitions and standards vary by region and change over time; verify the convention that applies to your case.
- Figures are only as accurate as the inputs you supply — check them before acting on the result.
- For work where the result carries real consequences, confirm it against an authoritative source.
Frequently Asked Questions
Free to use, no account needed. Calculations run in your browser, so nothing you type is sent to a server. Results are estimates — how we build and check our calculators.