1. What Is Common Difference?

The common difference (d) is a fundamental concept in arithmetic sequences. It represents the constant amount that each term increases or decreases by from the previous term in the sequence.

2. How Does The Calculator Work?

The calculator uses the common difference formula:

Where:

• \( d \) — Common difference
• \( a_{n} \) — The nth term in the sequence
• \( a_{n-1} \) — The previous term in the sequence

Explanation: The formula calculates the constant difference between consecutive terms in an arithmetic sequence.

3. Importance Of Common Difference

Details: The common difference is essential for identifying arithmetic sequences, predicting future terms, and understanding the pattern of progression in numerical sequences.

4. Using The Calculator

Tips: Enter any two consecutive terms from an arithmetic sequence. The calculator will determine the common difference between them.

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 the entire sequence.

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

Q3: What if the common difference is zero?
A: A common difference of zero means all terms in the sequence are equal, creating a constant sequence.

Q4: How is common difference related to linear functions?
A: In an arithmetic sequence, the common difference corresponds to the slope of the linear function that represents the sequence.

Q5: Can I find any term in the sequence using the common difference?
A: Yes, with the common difference and any term, you can find any other term using the formula: a_n = a_1 + (n-1)d