Free Tool

📊 Sequence Analyzer

Discover Hidden Patterns in Number Sequences

Enter Your Sequence

Enter numbers separated by commas (e.g., 1, 1, 2, 3, 5, 8, 13)

Analysis Results

Basic Information

Pattern Detection

🧮 Next Term Calculator

Calculate any term in this sequence based on the detected pattern

Calculate term n =

Result:

Differences Analysis

Ratios Analysis

Polynomial Analysis

Common Sequence Types

Arithmetic

2, 5, 8, 11, 14...

Constant difference between terms

a_n = a₁ + (n-1)d

Geometric

2, 6, 18, 54, 162...

Constant ratio between terms

a_n = a₁ × r^n-1

Fibonacci

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

Each term is sum of previous two

F_n = F_n-1 + F_n-2

Squares

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

Perfect squares

a_n = n²

Cubes

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

Perfect cubes

a_n = n³

Triangular

1, 3, 6, 10, 15...

Sum of first n natural numbers

a_n = n(n+1)/2

About Sequence Analysis

A number sequence is an ordered list of numbers that follows a specific pattern or rule. Understanding sequences is fundamental to mathematics, computer science, and many real-world applications.

💡 How to Use This Tool

Enter your sequence - Type numbers separated by commas
Click Analyze - The tool will detect patterns automatically
Review the results - See basic stats, pattern type, and formula
Use the Calculator - Find the next term in the sequence

🎓 Real-World Applications

Finance: Compound interest, loan amortization
Nature: Fibonacci spirals in shells, plant growth patterns
Computer Science: Algorithm complexity, data structures
Physics: Wave patterns, radioactive decay
Music: Rhythm patterns, harmonic sequences

📚 Tips for Pattern Recognition

Look for constant differences (arithmetic)
Check for constant ratios (geometric)
Try adding consecutive terms (Fibonacci-like)
Look at powers of n (n², n³, 2ⁿ)
Calculate second-order differences for polynomial sequences