Geometric Series Sum Calculator
Verified Calculation Engine
The online Geometric Series Sum 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.
Calculates sum of first n terms of geometric series: S_n = a(r^n - 1)/(r - 1) for r ≠ 1, or S_n = na for r = 1.
S_n = a(r^n - 1)/(r - 1) for r ≠ 1
S_n = na for r = 1
S_n = a(1 - r^n)/(1 - r) (alternative form)
Sum of finite geometric series
Inputs
Results
Worked Examples
Example 1: Basic
Find sum of first 5 terms of GP: 2, 6, 18, 54, ...
- firstTerm: 2
- commonRatio: 3
- n: 5
- sum: 242
- formula: S_5 = 2(3^5 - 1)/(3 - 1) = 2 × 242 / 2 = 242
Example 2: Board Level
Find sum of first 6 terms of GP: 5, -10, 20, -40, ...
- firstTerm: 5
- commonRatio: -2
- n: 6
- sum: -105
- formula: S_6 = 5[(-2)^6 - 1]/(-2 - 1) = 5 × 63 / (-3) = -105
About this calculator
Overview
Geometric Series Sum Calculator evaluates Geometric Series Sum for the math / sequences-series library. Primary input cue: First Term a [required]: First term. Method anchor: S_n = a(r^n - 1)/(r - 1) for r ≠ 1 S_n = na for r = 1 S_n = a(1 - r^n)/(1 - r) (alternative form). Sum of finite geometric series.
When to use
Reach for Geometric Series Sum Calculator to compare scenarios by changing one input at a time for geometric series sum.
Inputs explained
- First Term a [required]: First term
- Common Ratio r [required]: Common ratio
- Number of Terms n [required]: Number of terms to sum
Formula / method
S_n = a(r^n - 1)/(r - 1) for r ≠ 1 S_n = na for r = 1 S_n = a(1 - r^n)/(1 - r) (alternative form). Sum of finite geometric series (calculator id: geometric-series-sum-calculator).
Worked example
Worked values: firstTerm = 2, commonRatio = 3, n = 5 → sum = 242, formula = S_5 = 2(3^5 - 1)/(3 - 1) = 2 × 242 / 2 = 242
Interpreting results
Cross-check with a simple numeric example before relying on extreme inputs for geometric series sum.
Assumptions
- Empty required inputs are not silently replaced with zeros for geometric series sum. [geometric-series-sum-calculator]
- Geometric Series Sum is computed only from the fields you enter on this calculator.
- Real-number arithmetic is used unless geometric series sum explicitly needs integers.
Limitations
- If multiple conventions exist for geometric series sum, this calculator uses the convention implemented in its engine path.
- This page does not provide a full textbook proof for every identity related to geometric series sum.
- Complex/branch cuts and undefined points are not always interactively annotated for geometric series sum.
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
S_n = a(r^n - 1)/(r - 1) for r ≠ 1 S_n = na for r = 1 S_n = a(1 - r^n)/(1 - r) (alternative form). Sum of finite geometric series (calculator id: geometric-series-sum-calculator).
Example Calculation
Worked values: firstTerm = 2, commonRatio = 3, n = 5 → sum = 242, formula = S_5 = 2(3^5 - 1)/(3 - 1) = 2 × 242 / 2 = 242
Frequently Asked Questions
What is Geometric Series Sum Calculator?
- Geometric Series Sum Calculator evaluates Geometric Series Sum for the math / sequences-series library. Primary input cue: First Term a [required]: First term. Method anchor: S_n = a(r^n - 1)/(r - 1) for r ≠ 1 S_n = na for r = 1 S_n = a(1 - r^n)/(1 - r) (alternative form). Sum of finite geometric series.
How does Geometric Series Sum Calculator work?
- S_n = a(r^n - 1)/(r - 1) for r ≠ 1 S_n = na for r = 1 S_n = a(1 - r^n)/(1 - r) (alternative form). Sum of finite geometric series (calculator id: geometric-series-sum-calculator).
Why use this Math Numbers calculator?
- Reach for Geometric Series Sum Calculator to compare scenarios by changing one input at a time for geometric series sum.