Geometric Sequence Calculator
Verified Calculation Engine
The online Geometric Sequence Calculator helps you calculate instantly and solve problems related to Sequences Series. This tool provides accurate results using standard formulas and step-by-step calculation; you can view the formula with example in the calculator where available. Whether you are a student, teacher, or professional, this calculator simplifies complex calculations and saves time. Enter the required values below and get instant results. Results are shown clearly, with optional step-by-step explanation where applicable. The tool is free to use and works in any modern browser—no download or installation required. Bookmark this page for quick access whenever you need reliable Math Numbers calculations.
Finds nth term and properties of geometric sequence: a_n = a × r^(n-1) where a is first term and r is common ratio.
nth term: a_n = a × r^(n-1)
where a = first term, r = common ratio
Sequence: a, ar, ar², ar³, ...
Geometric sequence has constant ratio between consecutive terms
Inputs
Results
Worked Examples
Example 1: Basic
Find 6th term of GP: 2, 6, 18, 54, ...
- firstTerm: 2
- commonRatio: 3
- n: 6
- nthTerm: 486
- sequence: 2, 6, 18, 54, 162, 486
- formula: a_6 = 2 × 3^(6-1) = 2 × 243 = 486
Example 2: Board Level
Find 8th term of GP: 5, -10, 20, -40, ...
- firstTerm: 5
- commonRatio: -2
- n: 8
- nthTerm: -640
- sequence: 5, -10, 20, -40, 80, -160, 320, -640
- formula: a_8 = 5 × (-2)^(8-1) = 5 × (-128) = -640
About this calculator
Overview
Geometric Sequence Calculator evaluates Geometric Sequence for the math / sequences-series library. Primary input cue: First Term a [required]: First term of sequence. Method anchor: nth term: a_n = a × r^(n-1) where a = first term, r = common ratio Sequence: a, ar, ar², ar³, .... Geometric sequence has constant ratio between consecutive ter.
When to use
Use this page when you need geometric sequence from known inputs and want a transparent arithmetic or symbolic check.
Inputs explained
- First Term a [required]: First term of sequence
- Common Ratio r [required]: Common ratio
- Term Number n [required]: Which term to find
Formula / method
nth term: a_n = a × r^(n-1) where a = first term, r = common ratio Sequence: a, ar, ar², ar³, .... Geometric sequence has constant ratio between consecutive terms (calculator id: geometric-sequence-calculator).
Worked example
Worked values: firstTerm = 2, commonRatio = 3, n = 6 → nthTerm = 486, sequence = [2, 6, 18, 54, 162, 486], formula = a_6 = 2 × 3^(6-1) = 2 × 243 = 486
Interpreting results
Cross-check with a simple numeric example before relying on extreme inputs for geometric sequence.
Assumptions
- Geometric Sequence is computed only from the fields you enter on this calculator. [geometric-sequence-calculator]
- The wired execution function for `geometric-sequence-calculator` is the source of numerical behavior.
- Real-number arithmetic is used unless geometric sequence explicitly needs integers.
Limitations
- Edge cases outside the intended domain of geometric sequence may error or look unstable—treat them as out of scope.
- If multiple conventions exist for geometric sequence, this calculator uses the convention implemented in its engine path.
- Complex/branch cuts and undefined points are not always interactively annotated for geometric sequence.
Important note
Educational mathematics tool. Check edge cases and domain restrictions when results look unexpected.
How to Use This Calculator
- Enter the required values in the input fields.
- Click the Calculate button.
- View the computed result instantly.
Formula Used
nth term: a_n = a × r^(n-1) where a = first term, r = common ratio Sequence: a, ar, ar², ar³, .... Geometric sequence has constant ratio between consecutive terms (calculator id: geometric-sequence-calculator).
Example Calculation
Worked values: firstTerm = 2, commonRatio = 3, n = 6 → nthTerm = 486, sequence = [2, 6, 18, 54, 162, 486], formula = a_6 = 2 × 3^(6-1) = 2 × 243 = 486
Frequently Asked Questions
What is Geometric Sequence Calculator?
- Geometric Sequence Calculator evaluates Geometric Sequence for the math / sequences-series library. Primary input cue: First Term a [required]: First term of sequence. Method anchor: nth term: a_n = a × r^(n-1) where a = first term, r = common ratio Sequence: a, ar, ar², ar³, .... Geometric sequence has constant ratio between consecutive ter.
How does Geometric Sequence Calculator work?
- nth term: a_n = a × r^(n-1) where a = first term, r = common ratio Sequence: a, ar, ar², ar³, .... Geometric sequence has constant ratio between consecutive terms (calculator id: geometric-sequence-calculator).
Why use this Math Numbers calculator?
- Use this page when you need geometric sequence from known inputs and want a transparent arithmetic or symbolic check.