Number Sequence Calculator

Predict the Next Number in a Pattern

This calculator analyzes a series of numbers to identify if it follows an arithmetic or geometric pattern. Once the pattern is identified, it predicts the next three numbers in the sequence. It's a fun tool for math enthusiasts and students learning about sequences.

The Formulas Explained

• Arithmetic Sequence: A sequence where the difference between consecutive terms is constant. This constant difference is called the common difference (d).
  • Formula: aₙ = a₁ + (n-1)d
• Geometric Sequence: A sequence where the ratio between consecutive terms is constant. This constant ratio is called the common ratio (r).
  • Formula: aₙ = a₁ * r^(n-1)

How to Use the Calculator

1. Enter Sequence: Input a series of numbers separated by commas (at least 3 numbers are recommended for pattern detection).
2. Predict: The calculator will analyze the sequence, identify the type (Arithmetic, Geometric, or Unknown), and display the next three terms if a pattern is found.

Real-World Examples

• Arithmetic Sequence: You enter 3, 7, 11, 15.

  • The calculator identifies a common difference of 4.
  • It predicts the next terms as 19, 23, 27.

• Geometric Sequence: You enter 2, 6, 18, 54.

  • The calculator identifies a common ratio of 3.
  • It predicts the next terms as 162, 486, 1458.

Frequently Asked Questions (FAQ)

• What if my sequence is not arithmetic or geometric? The calculator will label it as 'Unknown'. There are many other types of sequences (like Fibonacci or quadratic sequences) that this basic tool does not detect.
• Can I use negative numbers or decimals? Yes, the calculator can handle sequences with negative numbers and decimals.
• Why does it need at least 2 or 3 numbers? With only one number, no pattern can be determined. With two numbers, it's impossible to distinguish between an arithmetic and a geometric sequence. Three numbers are usually needed to confirm a simple pattern.