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Arithmetic and Geometric Sequences — result sheet
nth term and partial sum of a sequence from its first term and difference or ratio.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Arithmetic: an = a1+(n-1)d, S = n/2*(2a1+(n-1)d). Geometric: an = a1*r^(n-1), S = a1*(r^n-1)/(r-1), S = a1*n when r = 1.
Closed forms give any term and the sum of the first n terms without listing them. The geometric r=1 case is handled separately to avoid dividing by zero.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Sequence type — 2 choices
- First term — minimum -1000000000; maximum 1000000000
- Difference or ratio — minimum -1000000000; maximum 1000000000
- Term count (n) — minimum 1; maximum 100000
Worked example
| Input | Value |
|---|---|
| Sequence type | arithmetic |
| First term | 2 |
| Difference or ratio | 3 |
| Term count (n) | 5 |
5th term 14; sum 40.
Assumptions and limits
- n is a positive whole number up to 100,000.
- Overflow beyond finite results is rejected.
- Real-number terms only.
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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