1. What is Arithmetic Sequence Common Difference?

The common difference (d) in an arithmetic sequence is the constant amount that each term increases or decreases by from the previous term. It is a fundamental property that defines the pattern of an arithmetic progression.

2. How Does the Calculator Work?

The calculator uses the arithmetic sequence common difference formula:

Where:

• \( d \) — Common difference (unit of sequence)
• \( term_{n+1} \) — Subsequent term in the sequence
• \( term_n \) — Current term in the sequence

Explanation: The common difference is calculated by subtracting any term from the term that follows it in the arithmetic sequence.

3. Importance of Common Difference Calculation

Details: Calculating the common difference is essential for understanding arithmetic sequences, predicting future terms, and solving problems involving linear patterns in mathematics and real-world applications.

4. Using the Calculator

Tips: Enter any two consecutive terms from your arithmetic sequence. The calculator will compute the common difference that defines the progression pattern.

5. Frequently Asked Questions (FAQ)

Q1: What is an arithmetic sequence?
A: An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant.

Q2: Can the common difference be negative?
A: Yes, a negative common difference indicates that the sequence is decreasing with each term.

Q3: How do I find other terms in the sequence?
A: Once you have the common difference, you can find any term using the formula: \( term_n = term_1 + (n-1) \times d \)

Q4: What if the sequence is not arithmetic?
A: If the difference between consecutive terms is not constant, the sequence is not arithmetic and this calculator may not provide meaningful results.

Q5: Can I use non-consecutive terms?
A: For non-consecutive terms, you would need to adjust the calculation: \( d = \frac{term_m - term_n}{m - n} \) where m and n are term positions.