1. What is Common Difference in Arithmetic Series?

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

2. How Does the Calculator Work?

The calculator uses the common difference formula:

Where:

• \( d \) — Common difference
• \( a_n \) — nth term of the sequence
• \( a_1 \) — First term of the sequence
• \( n \) — Number of terms

Explanation: The formula calculates the constant difference between terms by dividing the total progression from first to last term by the number of intervals between terms.

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 calculating series sums.

4. Using the Calculator

Tips: Enter any three known values from an arithmetic sequence to find the common difference. Number of terms (n) must be ≥ 2.

5. Frequently Asked Questions (FAQ)

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

Q2: How is common difference related to slope?
A: In graphical terms, the common difference represents the slope of the line formed by plotting the sequence terms.

Q3: What if I know two consecutive terms?
A: The difference between any two consecutive terms directly gives you the common difference (d = a₂ - a₁).

Q4: Can common difference be a fraction?
A: Yes, the common difference can be any real number - integer, fraction, or decimal.

Q5: How does common difference affect the sequence?
A: Larger absolute values of d mean terms change more rapidly. Positive d creates increasing sequences, negative d creates decreasing sequences.