Number Sequence Solver

What is a Number Sequence?

A number sequence is an ordered list of numbers that follow a specific pattern or rule. Identifying the pattern allows you to predict future terms in the sequence.

Types of Sequences

Arithmetic Sequences

Each term differs from the previous by a constant amount (the common difference). Example: 3, 7, 11, 15, 19... (difference of 4)

Geometric Sequences

Each term is multiplied by a constant ratio. Example: 2, 6, 18, 54... (ratio of 3)

Fibonacci Sequence

Each term is the sum of the two preceding terms. Example: 1, 1, 2, 3, 5, 8, 13...

Quadratic Sequences

The second differences are constant. Example: 1, 4, 9, 16, 25... (squares)

Prime Numbers

Numbers only divisible by 1 and themselves. Example: 2, 3, 5, 7, 11, 13...

Sequences in Geocaching

Number sequences frequently appear in geocaching puzzles:

• Coordinate puzzles: Find the pattern to get coordinates
• Multi-caches: Each stage gives a number in a sequence
• Missing terms: Fill in blanks to decode a message
• Mathematical themes: Famous sequences like Fibonacci

How to Identify Patterns

1. Calculate differences: Subtract consecutive terms
2. Calculate ratios: Divide consecutive terms
3. Check second differences: For quadratic patterns
4. Look for famous sequences: Primes, Fibonacci, squares
5. Try OEIS: The Online Encyclopedia of Integer Sequences

Tips for Solving

• Enter at least 4-5 terms for better pattern detection
• Check if numbers are special (primes, squares, etc.)
• Multiple patterns may match short sequences
• Consider letter-number conversions (A=1, B=2...)