Calculator
Enter the first term and any two of these values: common difference, last term, or number of terms.
Formula Used
An arithmetic sequence changes by a constant amount between consecutive terms. That constant amount is called the common difference.
Nth term: an = a1 + (n - 1)d
Sum of first n terms: Sn = n/2 × [2a1 + (n - 1)d]
Alternative sum form: Sn = n/2 × (a1 + an)
These formulas let you find missing terms, evaluate any position, calculate totals, and verify whether a list follows linear growth.
How to Use This Calculator
- Enter the first term of the sequence.
- Fill any two among common difference, last term, and number of terms.
- Optionally enter a target position for a specific term.
- Choose how many generated terms to display.
- Set decimal precision if needed.
- Press Calculate Sequence to view the results above the form.
- Review the table, formulas, and graph.
- Use the export buttons to save the results as CSV or PDF.
Example Data Table
| Scenario | First Term | Difference | Terms | Last Term | Sum |
|---|---|---|---|---|---|
| Weekly savings increase | 10 | 5 | 8 | 45 | 220 |
| Classroom seat rows | 12 | 2 | 10 | 30 | 210 |
| Pattern practice set | 3 | 3 | 6 | 18 | 63 |
FAQs
1. What is an arithmetic sequence?
An arithmetic sequence is a list of numbers where every new term changes by the same fixed amount. That fixed amount is called the common difference.
2. What does the common difference mean?
The common difference shows how much each term increases or decreases from the previous one. A positive value means growth, while a negative value means decline.
3. Can this calculator find a missing difference?
Yes. If you provide the first term, last term, and number of terms, the calculator derives the common difference automatically using the standard sequence formula.
4. Can it calculate the sum quickly?
Yes. The calculator uses the arithmetic series sum formula, which is faster and more accurate than manually adding every term one by one.
5. What happens if the values are inconsistent?
The calculator checks whether the inputs can produce a valid sequence. If the values conflict, such as impossible term counts, it shows a clear validation message.
6. Can I use decimals and negative values?
Yes. Decimal inputs and negative differences work correctly. This is useful for financial steps, temperature drops, measurement changes, or patterned decreases.
7. Why does the graph matter?
The graph helps you see the linear pattern immediately. Rising, falling, or constant behavior becomes easier to understand than reading only a numeric table.
8. When should I download CSV or PDF?
Use CSV when you want spreadsheet analysis or record keeping. Use PDF when you need a printable report for homework, notes, client work, or documentation.