Sequence Calculator
This is an arithmetic sequence tool: enter the first term, the common difference, and a term number to get the nth term and the sum of the first n terms. It handles only arithmetic sequences, not geometric ones.
What this calculator does
The Sequence Calculator estimates your result instantly from the values you enter, using standard math & conversions formulas. This is an arithmetic sequence tool: enter the first term, the common difference, and a term number to get the nth term and the sum of the first n terms. It handles only arithmetic sequences, not geometric ones. 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 Sequence Calculator
The Sequence Calculator works on arithmetic sequences, where each term increases by a fixed common difference. From the first term, the common difference, and a term number n, it returns the nth term and the sum of the first n terms. It does not handle geometric or other sequence types.
Use it to find a specific term or a running total in a sequence that grows by a constant step.
Formula & Mathematical Calculation
nth Term = f(First Term (a1), Common Difference (d), Term Number (n))
Calculated according to standard math formulas implemented in the calculator core.
Calculation Example
Enter First Term (a1) = 3, Common Difference (d) = 5, and Term Number (n) = 10, then click Calculate.
The tool shows nth Term = 48 and Sum of n Terms = 255, with the note "nth term = a + (n-1)d = 48; sum = 255."
Key Benefits
- Finds the nth term of an arithmetic sequence with a + (n-1)d
- Computes the sum of the first n terms in the same step
- Accepts a decimal or negative common difference
- Requires at least one term, guarding against invalid n
How to Use this Calculator
-
Enter the first term
Type the starting value of the sequence into the First Term (a1) field, for example 3. -
Enter the common difference
Type the fixed step between terms into the Common Difference (d) field, for example 5. -
Enter the term number and calculate
Type which term you want in the Term Number (n) field, click Calculate, and read the nth Term and Sum of n Terms boxes.
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
- 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
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.