Geometric Sequence
Find the nth term and finite sum when every term is multiplied by the same ratio. Negative and zero ratios are supported.
How to use Geometric Sequence
- Enter “First term”, using the units and limits shown in its label.
- Enter “Common ratio”, using the units and limits shown in its label.
- Enter “Number of terms (1–10,000)”, using the units and limits shown in its label.
- Select Calculate or Process. Review the result and any validation message before copying or downloading available output. Reset clears the result and restores the starting inputs.
Method & assumptions
Nth = first × ratio^(n−1); sum is the total of the first n terms.
Worked example
2, 6, 18, 54 has fourth term 54 and sum 80.
Results and projections are informational estimates, not financial, medical, legal, tax, or property advice. Check assumptions, units, rounding, and local requirements independently. Investment illustrations do not guarantee returns. Keep original files and check transformed output before use.
Questions, answered
Does a ratio of 1 work?
Yes. The sum is n times the first term; the implementation avoids the division-by-zero problem of the closed-form formula.
Where does this calculation run?
It runs locally in your browser. Enter plain numbers without currency symbols or thousands separators; use the same currency and measurement units throughout unless a converter explicitly asks for units.