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Finite Geometric Series Sum Calculator — result sheet
Calculate the final term and total of a finite geometric series.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: aₙ=a₁r^(n−1); Sₙ=a₁(rⁿ−1)/(r−1) for r≠1, and Sₙ=na₁ for r=1.
The handler keeps the r=1 case explicit instead of dividing by zero, while negative ratios remain visible through the final-term sign.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- First term a₁ — minimum -1000000000000; maximum 1000000000000
- Common ratio r — minimum -1000000; maximum 1000000
- Number of terms n — minimum 1; maximum 1000
Worked example
| Input | Value |
|---|---|
| First term a₁ | 3 |
| Common ratio r | 2 |
| Number of terms n | 5 |
Final term =48; sum =93.
Assumptions and limits
- The number of terms is a positive whole number.
- The ratio is constant and finite.
- This is a finite sum; convergence of an infinite series is handled separately.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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