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Arithmetic Series Sum Calculator — result sheet
Calculate the final term and total of a finite arithmetic series.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: aₙ=a₁+(n−1)d; Sₙ=n(a₁+aₙ)/2.
The last term and average-of-endpoints formula show both the progression and the total without listing every term.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- First term a₁ — minimum -1000000000000; maximum 1000000000000
- Common difference d — minimum -1000000000000; maximum 1000000000000
- Number of terms n — minimum 1; maximum 1000000
Worked example
| Input | Value |
|---|---|
| First term a₁ | 3 |
| Common difference d | 4 |
| Number of terms n | 10 |
Final term =39; sum =210.
Assumptions and limits
- The number of terms is a positive whole number.
- The difference is constant across the finite sequence.
- Infinite-series behavior is 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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