1. What Is The Recursive Rule For Arithmetic Sequence?

An arithmetic sequence is a sequence where each term after the first is found by adding a constant value (common difference) to the previous term. The recursive formula expresses each term in relation to the previous term.

2. How Does The Calculator Work?

The calculator uses the recursive formula for arithmetic sequences:

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: The calculator also uses the explicit formula aₙ = a₁ + (n-1) × d to directly compute any term without calculating all previous terms.

3. Importance Of Recursive Formulas

Details: Recursive formulas are fundamental in mathematics and computer science. They define sequences, model real-world phenomena, and form the basis of recursive algorithms and mathematical induction.

4. Using The Calculator

Tips: Enter the first term (a₁), common difference (d), and the term number (n) you want to calculate. The calculator will provide both the result and step-by-step solution.

5. Frequently Asked Questions (FAQ)

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

Q2: Can this calculator handle geometric sequences?
A: No, this calculator is specifically designed for arithmetic sequences with a constant difference between terms.

Q3: What if the common difference is negative?
A: The calculator works with negative differences, which would create a decreasing arithmetic sequence.

Q4: Are there limitations to recursive formulas?
A: Recursive formulas require knowing previous terms, making them less efficient for calculating distant terms compared to explicit formulas.

Q5: Can I calculate multiple terms at once?
A: This calculator calculates one specific term. For multiple terms, you would need to calculate each term sequentially.