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Common Difference Formula:
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The common difference is a key concept in arithmetic sequences. It represents the constant amount that each term increases or decreases by from the previous term. In an arithmetic progression, the difference between any two consecutive terms is always the same.
The calculator uses the common difference formula:
Where:
Explanation: The formula calculates the constant difference between consecutive terms in an arithmetic sequence by comparing the first and nth terms and accounting for the number of intervals between them.
Details: The common difference is fundamental to understanding arithmetic sequences and progressions. It helps in predicting future terms, finding missing terms, and analyzing patterns in numerical sequences. This concept is widely used in mathematics, finance, computer science, and various real-world applications.
Tips: Enter the nth term value, the first term value, and the term number (n must be greater than 1). The calculator will compute the common difference. All values must be valid numbers.
Q1: What if the common difference is negative?
A: A negative common difference indicates a decreasing arithmetic sequence where each term is smaller than the previous one.
Q2: Can the common difference be zero?
A: Yes, a common difference of zero means all terms in the sequence are equal, creating a constant sequence.
Q3: What's the relationship between common difference and slope?
A: In the graph of an arithmetic sequence, the common difference corresponds to the slope of the line connecting the points.
Q4: How is common difference used in real life?
A: It's used in financial calculations (like regular savings), physics (constant acceleration), and computer algorithms that involve regular increments.
Q5: What if I know two consecutive terms instead of the first and nth?
A: If you know any two consecutive terms, the common difference is simply their difference (a₂ - a₁, a₃ - a₂, etc.).