MATH

Geometric Sequence Calculator

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Find a numbered term and a finite partial sum for a constant-ratio sequence.

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Next steps

Choose a related calculation for your next question. Enter your values on the next page.

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On this page How it works & practical examples

How to use the Geometric Sequence Calculator

The first term is indexed one. Signed ratios are allowed, so a negative ratio alternates signs. A zero ratio keeps the first term and makes later terms zero.

The calculation

an = a1 r^(n−1); Sn = a1(1−r^n)/(1−r), with Sn = n a1 when r = 1

Worked example

Starting at 3 with ratio 2, the fifth term is 48 and the five-term sum is 93.

Assumptions and limits

Large powers can exceed the supported number range and are rejected. Only finite sums are calculated; no infinite-series convergence is inferred.

Common questions

Which inputs should I use?