Geometric Series Sum Calculator
Calculate the sum of a geometric sequence from its first term, common ratio and number of terms, free in your browser.
Enter Values
Minimum 1
How to use this calculator
- Enter the first term, common ratio and number of terms.
- Read the last term and the sum.
How it works
Each term multiplies by the common ratio. Last term = a·r^(n−1); sum = a·(1 − r^n) / (1 − r) when r ≠ 1.
Worked example
a=3, r=2, n=5. Terms 3, 6, 12, 24, 48 — sum 93.
Common mistakes
- Using a difference instead of a ratio — that's an arithmetic series.
- Expecting a finite sum for |r| ≥ 1 over infinite terms (only |r| < 1 converges).
Frequently asked questions
How do I sum a geometric series?
Sum = a × (1 − r^n) ÷ (1 − r) for n terms. If the ratio's magnitude is below 1, an infinite series converges to a ÷ (1 − r).
When does a geometric series have a finite total?
An infinite geometric series converges only when the common ratio's magnitude is less than 1.
What if the ratio is 1?
Then every term equals the first, so the sum is simply a × n.
Related tools
- Arithmetic Series Sum Calculator
- Arithmetic Sequence Calculator
- Geometric Sequence Calculator
- Fibonacci Calculator
- Angle Sum Calculator
- Average (Mean) Calculator
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Cite this tool
Zerdly. (2026). Geometric Series Sum Calculator. Retrieved from https://www.zerdly.com/tools/geometric-series-sum-calculator/
Tip: Enter any known values to calculate the remaining results.
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