Enter Sequence Details
Use commas, spaces, or line breaks between values.
Example Data Table
| Example Sequence | Detected Type | Rule | Next Terms |
|---|---|---|---|
| 4, 9, 14, 19, 24 | Arithmetic | Add 5 each step | 29, 34, 39 |
| 3, 6, 12, 24, 48 | Geometric | Multiply by 2 each step | 96, 192, 384 |
| 1, 4, 9, 16, 25 | Quadratic | Square-number growth | 36, 49, 64 |
| 2, 3, 5, 8, 13 | Recursive Additive | Add the previous two terms | 21, 34, 55 |
Formula Used
Arithmetic pattern: When first differences stay constant, the term rule is aₙ = a₁ + (n - 1)d.
Geometric pattern: When ratios stay constant, the term rule is aₙ = a₁r^(n - 1).
Quadratic pattern: When second differences stay constant, the sequence follows a quadratic form aₙ = an² + bn + c.
Recursive additive pattern: When each term equals the sum of the previous two, the rule is aₙ = aₙ₋₁ + aₙ₋₂.
Tolerance check: The calculator compares actual terms with model terms. Smaller error means a stronger match.
How to Use This Calculator
- Enter at least three numbers from the sequence.
- Choose auto detection or force a specific sequence type.
- Set the starting index if your first term is not at 1.
- Choose how many future terms you want to forecast.
- Enter any index for evaluating a specific term value.
- Adjust precision and tolerance for cleaner or stricter matching.
- Press Analyze Pattern to see the result above the form.
- Use the export buttons to download the projection table as CSV or PDF.
FAQs
1. What does this calculator detect?
It checks common sequence families such as arithmetic, geometric, quadratic, and recursive additive patterns. It also shows differences, ratios, formulas, forecasts, and a projected table.
2. Why do I need at least three terms?
Three values give the calculator enough structure to compare multiple models. Fewer values usually create too many valid possibilities for reliable pattern recognition.
3. What does tolerance mean?
Tolerance controls how closely the input must match a model. Smaller tolerance is stricter. Larger tolerance allows slight rounding noise or measurement variation.
4. Can this calculator handle decimals and negative values?
Yes. Decimal sequences, negative differences, and negative ratios can be analyzed. Very irregular data may still produce only a closest-match result instead of a strong match.
5. What is the starting index used for?
Starting index labels the first entered term. This is useful when the sequence begins at n = 0, n = 1, or any custom index required by your worksheet.
6. Why might auto detect choose the wrong pattern?
Some sequences fit more than one simple model over a short range. For example, a short arithmetic run may also look quadratic. You can force a mode when needed.
7. Does the PDF include the full projection table?
Yes. The PDF export prints the projected results table with indices, values, row type, differences, and ratios for easier review or sharing.
8. Can I use this for classroom and exam practice?
Yes. It is useful for homework checks, worksheet preparation, teaching demonstrations, and pattern verification before solving sequence questions manually.