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Number Sequence Pattern Detector

Analyze, identify, and predict number sequence patterns

Detect Sequence Pattern

Enter a number sequence to identify its pattern type

Separate numbers with commas, spaces, or new lines

Quick Examples

Try these common sequence patterns

Sequence Analyzer

Deep analysis with difference tables and statistics

Sequence Predictor

Predict future terms based on detected patterns

Find Specific Term (Nth Term)

Sequence Generator

Generate sequences from various formulas and patterns

Common Sequences Reference

Formulas and examples of well-known sequences

Arithmetic Sequence
aₙ = a₁ + (n-1)d

Example: 2, 5, 8, 11, 14... (d = 3)

Geometric Sequence
aₙ = a₁ × r^(n-1)

Example: 3, 6, 12, 24, 48... (r = 2)

Fibonacci Sequence
Fₙ = Fₙ₋₁ + Fₙ₋₂

1, 1, 2, 3, 5, 8, 13, 21, 34...

Triangular Numbers
Tₙ = n(n+1)/2

1, 3, 6, 10, 15, 21, 28...

Square Numbers
aₙ = n²

1, 4, 9, 16, 25, 36, 49...

Cube Numbers
aₙ = n³

1, 8, 27, 64, 125, 216...

How Pattern Detection Works
Arithmetic Detection

Checks if differences between consecutive terms are constant.

Geometric Detection

Checks if ratios between consecutive terms are constant.

Polynomial Detection

Uses difference tables to determine polynomial degree.

Recursive Detection

Identifies patterns where terms depend on previous terms.

Famous Sequences (OEIS)
A000040 Prime Numbers: 2, 3, 5, 7, 11, 13...
A000045 Fibonacci: 0, 1, 1, 2, 3, 5, 8...
A000217 Triangular: 1, 3, 6, 10, 15, 21...
A000290 Squares: 1, 4, 9, 16, 25, 36...
A000578 Cubes: 1, 8, 27, 64, 125...
A000079 Powers of 2: 1, 2, 4, 8, 16, 32...
A000142 Factorial: 1, 1, 2, 6, 24, 120...
A000108 Catalan: 1, 1, 2, 5, 14, 42, 132...

Understanding Number Sequences

What is a Number Sequence?

An ordered list of numbers following a specific pattern or rule.

  • Each term has a unique position (index)
  • Terms follow a predictable pattern
  • Can be finite or infinite
  • Used in mathematics, science, finance
Pattern Types

Common patterns include arithmetic, geometric, and recursive.

  • Arithmetic: constant difference
  • Geometric: constant ratio
  • Polynomial: follows n², n³, etc.
  • Recursive: depends on prior terms
Real-World Applications

Sequences appear in many practical contexts.

  • Financial: compound interest
  • Science: population growth
  • Computing: algorithms
  • Nature: Fibonacci spirals