Math & Conversions

Arithmetic Sequence Calculator

The Arithmetic Sequence Calculator finds the nth term and the sum of the first n terms of an arithmetic sequence from its first term, common difference, and number of terms.

What this calculator does

The Arithmetic Sequence Calculator estimates your result instantly from the values you enter, using standard math & conversions formulas. The Arithmetic Sequence Calculator finds the nth term and the sum of the first n terms of an arithmetic sequence from its first term, common difference, 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.

Arithmetic Sequence Calculator

Result

0
nth Term
0
Sum of First n Terms

About Arithmetic Sequence Calculator

An arithmetic sequence increases (or decreases) by the same amount, the common difference, at each step. Given the first term a1, the common difference d, and the number of terms n, the nth term is an = a1 + (n − 1)·d, and the sum of the first n terms is Sn = (n ÷ 2)·(2·a1 + (n − 1)·d).

Enter the three values and the calculator returns the nth term and the running sum, along with a chart of the sequence.

Formula & Mathematical Calculation

an = a1 + (n - 1) × d

sumN = (n ÷ 2) × (2 × a1 + (n - 1) × d)

Derived directly from the verified calculation function in the tool engine.

Calculation Example

For a first term of 3, a common difference of 5, and 10 terms: the 10th term is 3 + (10 − 1) × 5 = 48, and the sum of the first 10 terms is (10 ÷ 2) × (2 × 3 + (10 − 1) × 5) = 5 × 51 = 255.

Key Benefits

  • Returns both the nth term and the sum of the first n terms
  • Works with negative and decimal values for the first term and common difference
  • Shows a chart of the sequence
  • Runs in your browser with no sign-up

How to Use this Calculator

  1. Enter the first term
    Type the first term of the sequence into the a1 field.
  2. Enter the common difference
    Type the amount added at each step into the common difference field.
  3. Enter the number of terms
    Type how many terms you want, as a whole number of at least 1.
  4. Calculate
    Press Calculate to see the nth term, the sum, and the sequence chart.

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 Sequence 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

The common difference is the fixed amount added to each term to get the next one. In the sequence 3, 8, 13, 18, the common difference is 5.

It uses the standard arithmetic-sum formula, Sn = (n / 2)(2a1 + (n - 1)d), where a1 is the first term, d is the common difference, and n is the number of terms.

Yes. A negative common difference produces a decreasing sequence, and the calculator handles it the same way.

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.