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Geometric Series Sum and Nth Term Calculator

S_n = a(1−rⁿ)/(1−r); S_∞ = a/(1−r) for |r|<1.

Calculates the nth term, finite sum, and infinite sum of a geometric series from the first term a and common ratio r. Infinite sum exists only when |r| < 1.

Nadia Almasri By Nadia Almasri
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

a_n = a × r^(n−1); S_n = a × (1−r^n)/(1−r); S_∞ = a/(1−r)

In depth

Calculates the nth term, finite sum, and infinite sum of a geometric series from the first term a and common ratio r. Infinite sum exists only when |r| < 1.