1. What is a Recursive Sequence?

A recursive sequence is a sequence where each term is defined as a function of the preceding term(s). The rule \( a_n = a_{n-1} + d \) defines an arithmetic sequence where each term increases by a constant difference.

2. How Does the Calculator Work?

The calculator uses the recursive formula:

Where:

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

Explanation: This formula calculates the next term in an arithmetic sequence by adding the common difference to the previous term.

3. Importance of Recursive Rules

Details: Recursive sequences are fundamental in mathematics, computer science, and various real-world applications such as financial modeling, population studies, and algorithm design.

4. Using the Calculator

Tips: Enter the previous term value and the common difference. The calculator will compute the next term in the sequence.

5. Frequently Asked Questions (FAQ)

Q1: What types of sequences use this recursive rule?
A: This rule specifically defines arithmetic sequences where the difference between consecutive terms is constant.

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 I need to calculate multiple terms?
A: You can use the result as the new previous term and calculate subsequent terms iteratively.

Q4: Are there limitations to recursive sequences?
A: While powerful, recursive definitions require knowing previous terms and may not provide a direct formula for the nth term without iteration.

Q5: How is this different from an explicit formula?
A: An explicit formula (like \( a_n = a_1 + (n-1)d \)) gives any term directly, while recursive formulas define terms relative to previous ones.