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Arithmetic Sequence Term and Sum Calculator — result sheet
Calculate a selected term and the finite sum of an arithmetic sequence from its first term and common difference.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: aₙ = a₁ + (n−1)d; Sₙ = n(2a₁ + (n−1)d)/2.
The term advances by a constant difference, and the finite sum uses the average of the first and last terms times the count.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- First term a₁ — minimum -1000000000; maximum 1000000000
- Common difference d — minimum -1000000000; maximum 1000000000
- Term number n — minimum 1; maximum 1000000
Worked example
| Input | Value |
|---|---|
| First term a₁ | 3 |
| Common difference d | 4 |
| Term number n | 10 |
10th term = 39; sum through 10th term = 210.
Assumptions and limits
- The term number is a positive whole number.
- Terms are modeled as real numbers with one constant difference.
- Rounding, divergent infinite sums, and recurrence errors are not considered.
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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