1. What is Common Difference in Sequences?

The common difference (d) is the constant difference between consecutive terms in an arithmetic sequence. It's a fundamental property that defines the pattern of the sequence.

2. How Does the Calculator Work?

The calculator uses the common difference formula:

Where:

• \( d \) — Common difference
• \( sequence \) — Array of numbers

Explanation: The calculator first calculates the difference between the first two terms, then verifies if this difference is consistent throughout the entire sequence.

3. Importance of Common Difference

Details: Identifying the common difference is crucial for:

• Determining if a sequence is arithmetic
• Predicting future terms in the sequence
• Calculating the nth term of the sequence
• Finding the sum of arithmetic sequences

4. Using the Calculator

Tips:

• Enter numbers separated by commas (e.g., 3,7,11,15)
• At least two numbers are required
• The calculator will verify if all consecutive differences match

5. Frequently Asked Questions (FAQ)

Q1: What makes a sequence arithmetic?
A: A sequence is arithmetic if the difference between consecutive terms is constant throughout.

Q2: Can the common difference be negative?
A: Yes, a negative common difference means the sequence is decreasing (e.g., 10,7,4,1,... with d=-3).

Q3: What if my sequence has only two numbers?
A: Two numbers always form an arithmetic sequence, as there's only one difference to consider.

Q4: How is common difference used in real-world applications?
A: It's used in financial calculations (regular payments), physics (regular time intervals), and computer science (array indexing).

Q5: What's the formula for the nth term using common difference?
A: \( a_n = a_1 + (n-1)d \), where \( a_1 \) is the first term and \( d \) is the common difference.