1. What Is A Recursive Rule?

A recursive rule defines each term of a sequence based on previous terms. The simplest form is an arithmetic sequence where each term equals the previous term plus a constant difference (d).

2. How Does The Calculator Work?

The calculator uses the recursive formula:

Where:

• \( a_n \) — The nth term of the sequence
• \( a_{n-1} \) — The previous term in the sequence
• \( d \) — The common difference between terms

Explanation: Starting from the initial term (a₁), each subsequent term is calculated by adding the common difference to the previous term.

3. Applications Of Recursive Sequences

Details: Recursive sequences are used in mathematics, computer science, finance (compound interest), physics (harmonic motion), and population modeling.

4. Using The Calculator

Tips: Enter the first term of your sequence, the common difference between terms, and how many terms you want to calculate. The calculator will generate the sequence step by step.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between recursive and explicit formulas?
A: Recursive formulas define terms based on previous terms, while explicit formulas calculate any term directly using its position in the sequence.

Q2: Can this calculator handle geometric sequences?
A: No, this calculator is specifically designed for arithmetic sequences with a constant difference. Geometric sequences use multiplication rather than addition.

Q3: What if my sequence has a variable difference?
A: This calculator assumes a constant difference. For sequences with variable differences, you would need a more complex recursive formula.

Q4: How many terms can I calculate?
A: The calculator is limited to 50 terms to ensure reasonable processing and display.

Q5: Can I use decimal values for the first term and difference?
A: Yes, the calculator supports decimal values with up to 4 decimal places of precision.