An algebraic pattern is a number sequence where each term follows a rule expressible as a formula. The two most common types are arithmetic and quadratic sequences.

How the Difference Method Works

To detect an arithmetic sequence, check whether all consecutive differences (first differences) are equal. To detect a quadratic sequence, compute the differences of the first differences (second differences) and check if those are equal. A constant second difference always signals a quadratic relationship.

Practical Applications

• Grade 9–12 algebra: identifying sequence types is a core skill in many curricula.
• Physics: uniformly accelerated motion produces quadratic position sequences.
• Finance: regular savings plans generate arithmetic cumulative totals.
• Computer science: recognising growth patterns helps analyse algorithm complexity.

Tips for Best Results

• Enter at least 4–5 terms for reliable quadratic detection.
• Use decimal values when needed — the tool handles non-integer sequences.
• If the tool cannot find a pattern, try extending the sequence or checking for typos.