CalculateMeasure

Math & Geometry

Geometric Sequence Calculator

Calculate the nth term and sum of the first n terms of a geometric sequence.

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Calculator guide

How to use the Geometric Sequence Calculator

Calculate the nth term and sum of the first n terms of a geometric sequence. Enter the requested values and select Calculate. The result and supporting values are produced locally in your browser.

Formula

aₙ = a₁r^(n − 1); Sₙ = a₁(1 − rⁿ)/(1 − r) for r ≠ 1

Worked example

For 2, 6, 18, 54, … the 5th term is 162 and the first 5 terms sum to 242.

What to keep in mind

  • A geometric sequence has a constant ratio between consecutive nonzero terms.

Methodology

This calculator uses deterministic arithmetic and performs the calculation locally in your browser. Verify assumptions, units, and source values for your specific use case.

Review standard: Level A · Standard formula. How calculator reviews work.

Frequently asked questions

What does this calculator calculate?

Calculate the nth term and sum of the first n terms of a geometric sequence.

How is the result calculated?

aₙ = a₁r^(n − 1); Sₙ = a₁(1 − rⁿ)/(1 − r) for r ≠ 1.

Can I use the result for an important decision?

Use the result as a calculation aid and verify the inputs, assumptions, and applicable professional or regulatory requirements before relying on it for an important decision.

Does CalculateMeasure store the values I enter?

The calculator performs its arithmetic in your browser. The calculator itself does not need to send your entered values to a server to produce the result.