Calculator Inputs
Example Data Table
| Sequence | Likely Rule | Formula Example |
|---|---|---|
| 3, 7, 11, 15, 19 | Arithmetic | a(n) = 3 + (n - 1) × 4 |
| 2, 6, 18, 54, 162 | Geometric | a(n) = 2 × 3^(n - 1) |
| 2, 5, 10, 17, 26 | Quadratic | a(n) = n^2 + 1 |
| 1, 1, 2, 3, 5, 8 | Recurrence | a(n) = a(n-1) + a(n-2) |
Formula Used
This calculator checks several sequence families and ranks the simplest strong match first. Arithmetic detection uses constant first differences. Geometric detection uses constant ratios. Polynomial detection uses finite differences plus coefficient solving. Recurrence detection solves linear relationships such as Fibonacci-style rules. When exact models fail, it returns the best approximate polynomial within your selected limit.
How to Use This Calculator
- Enter at least three sequence terms using commas, spaces, or semicolons.
- Set the starting index to match your notation.
- Choose the maximum polynomial degree and recurrence order you want checked.
- Adjust tolerance if your values are rounded decimals.
- Pick how many future terms you want predicted.
- Click Find Formula to view the best detected rule, graph, differences, and export options.
FAQs
1. What kinds of sequence rules can this page detect?
It checks arithmetic, geometric, polynomial, and linear recurrence patterns. If none match exactly, it reports the strongest approximate polynomial allowed by your selected degree setting.
2. Why can different formulas fit the same short sequence?
Short lists may support multiple valid rules. This page ranks simpler exact patterns first because they are usually more interpretable and more likely to generalize beyond the entered terms.
3. What does tolerance do?
Tolerance controls how strict the equality checks are. Smaller values demand near-perfect matches. Larger values help when sequence terms are rounded, measured, or slightly noisy.
4. When should I use a starting index of 0?
Use 0 when your sequence naturally begins at n = 0, such as many programming and recurrence definitions. Use 1 when your textbook or worksheet starts at n = 1.
5. Can the calculator handle decimal sequences?
Yes. Decimal entries work well, especially when you set an appropriate tolerance. That helps the detector identify underlying patterns despite rounding or measurement limitations.
6. Why is the result marked approximate?
That means no tested exact family matched every term within tolerance. The page then chooses the best least-squares polynomial model from your selected degree range.
7. What does the graph show?
The Plotly chart compares observed terms with projected terms. It helps you see whether the rule is growing linearly, exponentially, or curving like a polynomial.
8. What is included in the CSV and PDF files?
Both exports include the detected classification, chosen formula, fit quality details, and the observed and predicted values table for quick reporting or sharing.