Find Sequence Calculator
Enter at least 2 terms of a sequence. The calculator will detect a likely pattern, estimate a formula, and generate future values.
What this sequence finder does
A sequence is an ordered list of numbers that follows a rule. Sometimes the rule is obvious (like adding 2 each step), and sometimes it is hidden behind multiple layers of differences. This calculator helps you quickly identify common patterns and predict future terms.
It is designed for students, teachers, and anyone working with number puzzles, algebra practice, coding challenges, or exam prep. You can use it to estimate missing terms, test your own pattern guesses, and build intuition for recursive and explicit rules.
How to use the calculator
- Type your known terms in order, such as 5, 10, 15, 20.
- Optionally enter a specific position n if you want the value at that term.
- Choose how many future terms to generate.
- Click Analyze Sequence.
The output includes the detected pattern, a rule/formula description, next terms, and the nth value when requested.
Patterns this calculator can detect
1) Arithmetic sequence
Each term changes by a constant difference d. Example: 4, 9, 14, 19 has d = 5.
Formula form: an = a1 + (n - 1)d.
2) Geometric sequence
Each term is multiplied by a constant ratio r. Example: 3, 6, 12, 24 has r = 2.
Formula form: an = a1 · rn - 1.
3) Quadratic sequence
If the second differences are constant, the sequence is modeled by a quadratic expression in n.
Example: 2, 6, 12, 20, 30 has first differences 4, 6, 8, 10 and constant second difference 2.
4) Fibonacci-style recurrence
Each term equals the sum of the previous two terms. Classic example: 1, 1, 2, 3, 5, 8...
5) Finite-difference continuation
When no simple common rule matches, the calculator uses a finite-difference table to extrapolate a consistent continuation from your data. This is often useful for puzzle-style sequences.
Tips for better results
- Provide at least 4-6 terms when possible.
- Make sure terms are in the correct order.
- Avoid mixing unrelated values from different patterns.
- Remember that many short sequences can fit more than one rule.
Important limitation
No sequence solver can guarantee the “one true rule” from a short list alone. Number patterns are often ambiguous. This tool gives a strong best guess based on common mathematical structures. If you are working on a classroom or contest problem, also use context clues from the question.