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Geometric Sequence Term and Sum Calculator — result sheet
Calculate a selected term and finite sum of a geometric sequence from its first term and common ratio.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: aₙ=a₁r^(n−1); finite sum=a₁(r^n−1)/(r−1) for r≠1, and n×a₁ for r=1.
The selected term and sum are returned with the ratio-one special case handled explicitly.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- First term a₁ — minimum -1000000; maximum 1000000
- Common ratio r — minimum -100; maximum 100
- Number of terms n — minimum 1; maximum 100
Worked example
| Input | Value |
|---|---|
| First term a₁ | 3 |
| Common ratio r | 2 |
| Number of terms n | 5 |
Fifth term =48; sum =93.
Assumptions and limits
- The first term and ratio are finite and the number of terms is a positive whole number.
- The sequence is finite and indexed from one.
- Infinite convergence, rounding of terms, symbolic recurrence, and application-specific meaning are not modeled.
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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