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Math Calculators

Geometric Series Sum Calculator

Verified formula Updated Jun 2026 Private — runs on your device

Enter details
Verified formula Private

Sum of the series

80.0000

Last term
54.0000

For general information only — not financial, tax, legal or medical advice. Verify before you rely on it.

How to use the Geometric Series Sum Calculator

The Geometric Series Sum Calculator works out your sum of the series, along with 1 related figure in an instant. Enter first term (a), common ratio (r) and number of terms (n) and the result updates as you type — it is free, needs no sign-up, and runs entirely in your browser so your figures stay private.

  1. Enter the first term (a).
  2. Enter the common ratio (r).
  3. Enter the number of terms (n).
  4. Read off your sum of the series, together with last term — the calculator updates automatically, with no button to press.

Worked example

For example, with first term (a) of 2, common ratio (r) of 3 and number of terms (n) of 4, the sum of the series is 80.0000.

Inputs used
First term (a) 2
Common ratio (r) 3
Number of terms (n) 4
Results
Sum of the series 80.0000
Last term 54.0000

Results are estimates for educational use, not professional advice.

Key terms explained

Ratio
A comparison of two quantities showing how many times one contains the other.

Frequently asked questions

It is the sum of a geometric sequence, where each term is the previous one times a fixed ratio. 2 + 6 + 18 + 54 sums to 80.

For ratio r not equal to 1, sum = a × (1 − rⁿ) ÷ (1 − r), where a is the first term and n the number of terms.

Every term equals the first term, so the sum is simply a × n.

Yes, but only when the ratio is between −1 and 1. Then the infinite sum is a ÷ (1 − r).

Enter the first term (a). Enter the common ratio (r). Enter the number of terms (n). Read off your sum of the series, together with last term — the calculator updates automatically, with no button to press.

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