1. What is Common Difference in Arithmetic Sequence?

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

2. How Does the Calculator Work?

The calculator uses the arithmetic sequence formula:

Where:

• \( d \) — Common difference
• \( a_n \) — Current term in the sequence
• \( a_{n-1} \) — Previous term in the sequence

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

3. Importance of Common Difference

Details: The common difference determines whether the sequence is increasing (d > 0), decreasing (d < 0), or constant (d = 0). It's essential for predicting future terms and understanding the sequence's behavior.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Can the common difference be zero?
A: Yes, a common difference of zero means all terms in the sequence are identical (constant sequence).

Q2: How is common difference related to slope?
A: In the graph of an arithmetic sequence, the common difference corresponds to the slope of the line formed by the sequence points.

Q3: Can the common difference be a fraction or decimal?
A: Absolutely, the common difference can be any real number - integer, fraction, or decimal.

Q4: How do I find the nth term using common difference?
A: The nth term can be found using: \( a_n = a_1 + (n-1)d \), where \( a_1 \) is the first term.

Q5: What if my sequence isn't arithmetic?
A: If the difference between consecutive terms isn't constant, the sequence isn't arithmetic and this calculator doesn't apply.