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Geometric sequence calculator

Find the nth term and the sum of a geometric sequence.

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The Geometric sequence calculator turns First term (a), Common ratio (r), Number of terms (n) into nth term, Sum of terms, instantly and for free. For instance, with First term (a) = 2, Common ratio (r) = 3 and Number of terms (n) = 8 it returns nth term = 4,374 and Sum of terms = 6,560.

How to use it

  1. Enter your values: First term (a), Common ratio (r), Number of terms (n).
  2. Read the result instantly: nth term, Sum of terms.

Frequently asked questions

How does the Geometric sequence calculator work?

It takes First term (a), Common ratio (r) and Number of terms (n) and derives nth term and Sum of terms from them. The calculation is live as you type, so the result updates on every change.

Which values does the calculator ask for?

3 values: First term (a), Common ratio (r) and Number of terms (n). Nothing else is required — no account, no file upload.

What does a typical calculation look like?

With First term (a) = 2, Common ratio (r) = 3 and Number of terms (n) = 8, the calculator returns nth term = 4,374 and Sum of terms = 6,560. Those figures come from running this exact tool, so you can reproduce them by entering the same values.

How much does the result change with different inputs?

It moves a lot. Using First term (a) = 4, Common ratio (r) = 6 and Number of terms (n) = 16 instead, nth term goes from 4,374 to 1,880,739,938,000 — which is why it is worth testing a few scenarios rather than trusting a single figure.

What does it give for smaller values?

Scaled down to First term (a) = 1, Common ratio (r) = 2 and Number of terms (n) = 4, nth term comes out at 8. The relationship is worth checking at both ends before you rely on a single result.

When would I actually use this?

Finding the nth term without listing every one before it, summing a long run in one step, and recognising which family a sequence belongs to.

What is the most common mistake?

Starting the index at the wrong end. Whether the first term is a₀ or a₁ shifts every result by one position, and the two conventions are both common.

What is the difference between the Geometric sequence calculator and the Arithmetic sequence calculator?

Both return nth term and Sum of terms. What differs is what they ask for: this one wants Common ratio (r), the Arithmetic sequence calculator wants Common difference (d). Use whichever matches the numbers you already have.

Is there a tool for the next step?

Geometric Distribution Calculator is the closest one after this: Compute the probability of the first success on trial k (or after k failures) from the per-trial success probability p.

What else is worth having open alongside it?

Geometric mean calculator and Graphical degree sequence validator — they come up in the same task often enough to be worth a second tab.

Further reading

All guides →
ExplainerGeometric vs Arithmetic Mean: Which to UseThe arithmetic mean adds and divides; the geometric mean multiplies and takes a root. Learn which fits growth rates, ratios, and averages.How-toHow to Find a Cube Root by HandA step-by-step guide to finding a cube root by estimation and refinement — plus how it differs from a square root and when a value stays irrational.ExplainerWhat Is a Percentile? The 90th Percentile ExplainedA percentile tells you where a value ranks within a group. Learn what the 90th percentile really means and why a percentile is not the same as a percentage.How-toHow to Calculate a Weighted AverageA weighted average gives some values more influence than others. Learn the Σ(w·x) / Σw formula with grade and portfolio examples you can follow step by step.ExplainerHow Exponents Work: Powers and the Laws of ExponentsAn exponent is repeated multiplication. Learn the laws of exponents, what negative and fractional powers mean, and why anything to the zero is one.How-toHow to Calculate Percent Error: The Accuracy Formula for SciencePercent error tells you how close a measurement is to the true value. Learn the formula, work through an example, and see how scientists use it to judge accuracy.
Geometric sequence calculator — OneKitly