Geometric Sequence Calculator
Find the nth term of a geometric sequence from the first term, common ratio, and term number, and list the sequence up to the first 30 terms.
What this calculator does
The Geometric Sequence Calculator estimates your result instantly from the values you enter, using standard math & conversions formulas. Find the nth term of a geometric sequence from the first term, common ratio, and term number, and list the sequence up to the first 30 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 Geometric Sequence Calculator
This calculator works with a geometric sequence, where each term is the previous one multiplied by a fixed common ratio. You enter the first term (a), the common ratio (r), and the term number (n).
It returns the nth term using a × rⁿ⁻¹ and lists the sequence itself. The listing shows up to the first 30 terms; beyond that it adds an ellipsis, while the nth term is still computed exactly for the n you choose.
Formula & Mathematical Calculation
Calculation Method
- Compute } m=Math.min(n,30),s=[]
Calculation Example
With first term a = 2, common ratio r = 3, and term number n = 6:
- nth term = a × rⁿ⁻¹ = 2 × 3⁵ = 2 × 243 = 486
- Sequence: 2, 6, 18, 54, 162, 486
The calculator reports an nth term of 486 and lists the sequence 2, 6, 18, 54, 162, 486.
Key Benefits
- Computes the nth term directly with a x r to the power of (n-1)
- Lists the sequence terms so you can see the pattern build
- Works with fractional and negative common ratios
How to Use this Calculator
-
Enter the first term
Type the starting value into the 'First Term (a)' field. -
Enter the common ratio
Type the ratio between consecutive terms into the 'Common Ratio (r)' field. -
Enter the term number and calculate
Type which term you want into the 'Term Number (n)' field and press Calculate to see the nth term and the sequence.
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
- Geometric 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.