Geometric Sequence Calculator
A geometric sequence multiplies each term by a constant ratio. This is a mathematical progression tool for schoolwork and patterns, not a financial return or interest calculator.
How to use this calculator
- Enter the first term, common ratio and term number. The page returns the selected term and finite sum.
- Check the labels and units before using a result outside this page.
- Change one input at a time if you want to compare scenarios.
Formula and method
aₙ = a₁rⁿ⁻¹; Sₙ = a₁(1 − rⁿ) ÷ (1 − r), for r ≠ 1
- aₙ = a₁rⁿ⁻¹; Sₙ = a₁(1 − rⁿ) ÷ (1 − r), for r ≠ 1
- Large ratios and term numbers can exceed the range of ordinary numeric representation.
Worked examples
Worked example
First term 2, ratio 3, and five terms.
The fifth term is 2 × 3⁴ = 162; the sum is 2 + 6 + 18 + 54 + 162 = 242.
The fifth term is 2 × 3⁴ = 162; the sum is 2 + 6 + 18 + 54 + 162 = 242.
Understanding the result
A geometric sequence multiplies each term by a constant ratio. This is a mathematical progression tool for schoolwork and patterns, not a financial return or interest calculator.
Large ratios and term numbers can exceed the range of ordinary numeric representation.
Important notes
Large ratios and term numbers can exceed the range of ordinary numeric representation.
Displayed outputs are rounded for readability; preserve full precision when continuing a calculation.
Frequently asked questions
What does this geometric sequence calculator show?
A geometric sequence multiplies each term by a constant ratio. This is a mathematical progression tool for schoolwork and patterns, not a financial return or interest calculator.
Which inputs should I check first?
Enter the first term, common ratio and term number. The page returns the selected term and finite sum.
Can the result be used as a final professional specification?
Large ratios and term numbers can exceed the range of ordinary numeric representation.
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Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
- How to Calculate Percent Error — Learn the percent error formula and how to compare an experimental value with a reference or accepted value.
This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.