1. What is Common Difference in Arithmetic Sequence?

The common difference (d) is the constant difference between consecutive terms in an arithmetic sequence. It determines how much each term increases or decreases from the previous term.

2. How Does the Calculator Work?

The calculator uses the common difference formula:

Where:

• \( a_n \) — The n-th term of the sequence
• \( a_1 \) — The first term of the sequence
• \( n \) — The position of the term in the sequence
• \( d \) — The common difference

Explanation: The formula calculates the constant difference between terms by dividing the total change from first to n-th term by the number of steps between them.

3. Importance of Common Difference

Details: The common difference is fundamental in arithmetic sequences as it allows prediction of any term in the sequence and helps in understanding the sequence's behavior.

4. Using the Calculator

Tips: Enter any three known values (aₙ, a₁, and n) to calculate the common difference. Ensure n is greater than 1.

5. Frequently Asked Questions (FAQ)

Q1: Can the common difference be negative?
A: Yes, a negative common difference means each term decreases by that amount.

Q2: What if the common difference is zero?
A: A zero common difference means all terms in the sequence are equal (constant sequence).

Q3: How is this different from geometric sequence?
A: In arithmetic sequences, terms change by addition (common difference), while in geometric sequences, terms change by multiplication (common ratio).

Q4: Can I find other terms using the common difference?
A: Yes, once you know d, you can find any term using: \( a_n = a_1 + (n-1)d \).

Q5: What are practical applications of arithmetic sequences?
A: Used in financial calculations (simple interest), physics (uniform motion), and many real-world patterns.