1. What is the Fibonacci Sequence?

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, starting from 0 and 1. It appears in many settings in mathematics and in nature.

2. How Does the Calculator Work?

The calculator uses the Fibonacci formula:

Where:

• \( F_n \) — Current Fibonacci number
• \( F_{n-1} \) — Previous number in sequence
• \( F_{n-2} \) — Number before the previous one

Explanation: Starting with your chosen initial values, each subsequent number is calculated by adding the two numbers before it.

3. Importance of Fibonacci Numbers

Details: Fibonacci numbers appear in computer algorithms, biological settings, financial markets, and have many mathematical properties.

4. Using the Calculator

Tips: Enter your starting two numbers and how many terms you want to calculate. The sequence will be generated from your starting values.

5. Frequently Asked Questions (FAQ)

Q1: What's the standard Fibonacci sequence?
A: The classic sequence starts with 0 and 1: 0, 1, 1, 2, 3, 5, 8, 13, etc.

Q2: Can I start with different numbers?
A: Yes! This calculator lets you start with any two numbers to create your own sequence.

Q3: How many terms can I calculate?
A: The calculator is limited to 50 terms for practical reasons.

Q4: What's the golden ratio connection?
A: The ratio between consecutive Fibonacci numbers approaches the golden ratio (1.618...) as the numbers get larger.

Q5: Where are Fibonacci numbers used?
A: They appear in algorithms, nature (like flower petals), architecture, and financial analysis.