Last updated October 10, 2026 · Report an error
A geometric series is the sum of a sequence where each term is a constant multiple of the one before it — these series can grow (or shrink) extremely quickly, making manual addition impractical for more than a few terms.
This calculator finds the sum of a geometric series directly from its first term, common ratio, and number of terms, with a full step-by-step solution.
How it works
Enter the first term, the common ratio between consecutive terms, and the number of terms in the series. The calculator finds the last (nth) term, then applies the geometric series sum formula to find the total.
- Enter first term (a).
- Enter common ratio (r).
- Enter number of terms (n).
- Click Calculate to see your results.
Examples
The sum of the first 6 terms starting at 2, tripling each time
With a first term of 2, a common ratio of 3, and 6 terms, the last term is 486 and the sum of the series is 728.
Who should use it
- Finding the total of a sequence of compounding or repeatedly-scaled values.
- Solving geometric series problems for coursework or exam preparation.
Industry applications
- Mathematics education
- Financial modeling involving compounding growth patterns
Advantages
- Calculates both the sum and the last term in one step.
- Includes a complete, formula-based step-by-step solution.
Limitations
- Only applies to geometric (constant-ratio) series, not arithmetic or other sequences.
Common mistakes to avoid
- Confusing the common ratio (what each term is multiplied by) with the common difference used in arithmetic series (what's added).
- Using a common ratio of exactly 1, which the standard formula can't handle (all terms are identical in that case).
Best practices
- Double-check whether your sequence is actually geometric (constant ratio) rather than arithmetic (constant difference) before using this calculator.
Tips
- A common ratio between -1 and 1 (exclusive) means the series would converge to a finite sum even as the number of terms grows toward infinity — a distinct related concept from this calculator's finite-term sum.