1. What is a Recursive Rule Formula?

A recursive rule formula defines a sequence where each term is determined by one or more of the previous terms. The general form is \( a_n = f(a_{n-1}) \), where f is a function that defines the relationship between consecutive terms.

2. How Does the Calculator Work?

The calculator implements the recursive formula:

Where:

• \( a_n \) — The current term in the sequence
• \( a_{n-1} \) — The previous term in the sequence
• \( f \) — The function defining the relationship between terms

Explanation: Starting from an initial value a₀, the calculator applies the function f repeatedly to generate subsequent terms in the sequence.

3. Applications of Recursive Sequences

Details: Recursive sequences are used in mathematics, computer science, physics, economics, and many other fields to model processes where each state depends on previous states.

4. Using the Calculator

Tips: Enter the initial value, number of iterations, select the function type, and provide the necessary parameter. The calculator will generate the sequence up to the specified number of terms.

5. Frequently Asked Questions (FAQ)

Q1: What types of recursive functions can I calculate?
A: The calculator supports linear, exponential, quadratic, and custom functions. Each requires different parameter inputs.

Q2: How many iterations can I calculate?
A: The calculator supports up to 100 iterations to ensure reasonable computation time.

Q3: Can I define my own custom function?
A: The current implementation offers a sample custom function. For more complex custom functions, the code would need to be modified.

Q4: What's the difference between recursive and explicit formulas?
A: Recursive formulas define terms relative to previous terms, while explicit formulas define each term directly in terms of n.

Q5: Are there limitations to this calculator?
A: The calculator is designed for educational purposes and may not handle extremely large numbers or complex functions optimally.