1. What is a Number Sequence?

A number sequence is an ordered list of numbers defined by a specific rule or pattern. Each number in the sequence is called a term, typically denoted as aₙ where n is the term's position.

2. How Does the Calculator Work?

The calculator computes the nth term of a sequence using the formula:

Where:

• \( a_n \) — The nth term of the sequence
• \( n \) — The position of the term in the sequence (positive integer)
• \( f \) — The function defining the sequence

Note: This example uses the Fibonacci sequence, but can be adapted for other sequences.

3. Importance of Sequence Calculation

Details: Sequence calculations are fundamental in mathematics, computer science, and many real-world applications like financial modeling and biological pattern recognition.

4. Using the Calculator

Tips: Enter a positive integer n to calculate the nth term of the sequence. The calculator will return the term value (unitless).

5. Frequently Asked Questions (FAQ)

Q1: What types of sequences can this calculate?
A: The current implementation calculates Fibonacci numbers, but can be modified for arithmetic, geometric, or other sequences.

Q2: What's the maximum n value I can enter?
A: The limit depends on your system's computational capacity. Very large n values may cause performance issues.

Q3: Why are sequence calculations important?
A: They help model growth patterns, solve recursive problems, and understand mathematical relationships.

Q4: Can I modify this for my own sequence?
A: Yes, by changing the calculation function in the PHP code.

Q5: Are there limitations to this calculator?
A: It's designed for single-term calculation. For sequence generation, you'd need a different implementation.