Geometric Sequence
Free Geometric Sequence calculator with clear step-by-step results.
About Geometric Sequence
A geometric sequence multiplies each term by a constant ratio.
Formula
Formula
g(n) = a × r^(n−1); sum = a(1−rⁿ)/(1−r)
Worked example
With the default values below, Geometric Sequence returns Term g(n) of 96.000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- First termminimum 0
- 3
- Common ratiominimum 0
- 2
- Term number nminimum 1
- 6
Results
- Term g(n)
- 96.000
- Sum of n Terms
- 189.000
- Ratio
- 2.000
Step by step
- 1Values used
- 2Formula
- 3Term g(n)= 96.000
- 4Sum of n Terms= 189.000
- 5Ratio= 2.000
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
How does this calculator work?
A geometric sequence multiplies each term by a constant ratio.
Why does this matter?
Terms grow exponentially when |r| > 1.