1. What is Common Difference?

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 an arithmetic sequence.

2. How Does the Calculator Work?

The calculator uses these formulas:

Where:

• \( first \) — First term of the sequence
• \( last \) — Last term of the sequence
• \( n \) — Number of terms in the sequence
• \( d \) — Common difference between terms

Explanation: The common difference is calculated by dividing the total span (last - first) by the number of intervals (n-1). The arithmetic mean of the first and last terms gives the middle term when n is odd.

3. Importance of Arithmetic Mean

Details: In an arithmetic sequence, the arithmetic mean of the first and last terms equals the mean of the entire sequence. This property is useful in various mathematical and statistical applications.

4. Using the Calculator

Tips: Enter the first term, last term, and number of terms (must be ≥2). The calculator will determine the common difference and arithmetic mean.

5. Frequently Asked Questions (FAQ)

Q1: What is an arithmetic sequence?
A: A sequence where each term after the first is found by adding a constant (the common difference) to the previous term.

Q2: Can the common difference be negative?
A: Yes, a negative common difference means the sequence is decreasing.

Q3: What if the number of terms is 1?
A: The concept of common difference doesn't apply to a single term. You need at least 2 terms.

Q4: How is arithmetic mean different from common difference?
A: The common difference shows how much terms increase/decrease, while the arithmetic mean gives the central value.

Q5: Can this be used for non-arithmetic sequences?
A: No, these formulas only work for arithmetic sequences where the difference between terms is constant.