Pattern Sequence Calculator

Paste values and detect hidden sequence structures. Review nth terms, differences, ratios, forecasts, and summaries. Designed for students, teachers, analysts, and curious problem solvers.

Calculator

Sequence values

Pattern mode

Predict next terms

Specific position

Starting position

Decimal places

Accepted inputs

Example data table

Input sequence	Detected type	Rule highlight	Next term
2, 4, 6, 8	Arithmetic	Common difference = 2	10
3, 9, 27	Geometric	Common ratio = 3	81
1, 4, 9, 16	Quadratic	Second difference is constant	25
1, 1, 2, 3, 5	Fibonacci-like	Each term uses the previous two	8

Formula used

This calculator checks several common sequence rules and then predicts future values from the best matching pattern or the manual model you choose.

Constant: a_n = c
Arithmetic: a_n = a_s + (n - s)d
Geometric: a_n = a_sr^(n-s)
Quadratic: a_n = an² + bn + c
Fibonacci-like: a_n = a_n-1 + a_n-2

First differences help confirm arithmetic patterns. Ratios help confirm geometric patterns. Constant second differences usually indicate a quadratic sequence. Recursive addition rules identify Fibonacci-like growth.

How to use this calculator

Enter sequence terms separated by commas, lines, semicolons, or bars.
Leave auto detect selected, or choose a manual rule.
Set how many future terms you want predicted.
Enter a specific position if you need one term.
Click calculate to show the result above the form.
Review the diagnostics, forecast table, and graph.
Use the CSV or PDF buttons to export results.

FAQs

1. What sequence types does this calculator support?

It supports constant, arithmetic, geometric, quadratic, and Fibonacci-like patterns. You can let it detect the rule automatically or force a pattern manually.

2. Can I enter decimal or negative numbers?

Yes. The parser accepts integers, decimals, and negative values. That helps when you work with signed growth, scaled measurements, or fractional progressions.

3. What does the specific position field do?

It estimates the term at the position you request. If the position already exists in your input, the calculator returns the given term.

4. Why are first and second differences shown?

Differences expose structure quickly. Equal first differences suggest arithmetic behavior. Equal second differences usually show a quadratic rule.

5. Why can a manual model show a note?

A note appears when your chosen model does not perfectly fit every entered value. The calculator still applies the selected rule for forecasting.

6. Can this tool solve every possible sequence?

No. Mixed, piecewise, symbolic, or higher-order patterns may need manual reasoning. This tool focuses on common numeric sequence families.

7. What is included in the export files?

The exports include the position table, term values, and source labels. That makes it easy to save or share forecasted results.

8. Is the graph useful for simple sequences?

Yes. A graph makes constant, linear, exponential, and quadratic growth easier to compare, especially when you extend several future terms.