1. What is an Arithmetic Sequence?

An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. This constant difference is called the common difference.

2. How Does the Calculator Work?

The calculator uses the arithmetic sequence formula:

Where:

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

Explanation: Each term is found by adding the common difference to the previous term.

3. Applications of Arithmetic Sequences

Details: Arithmetic sequences are used in financial calculations, physics, computer science, and many real-world scenarios involving regular intervals or constant rates of change.

4. Using the Calculator

Tips: Enter the first term, common difference, and term number you want to find. All values must be valid (term number must be positive integer).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between arithmetic and geometric sequences?
A: Arithmetic sequences have a constant difference between terms, while geometric sequences have a constant ratio.

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

Q3: What if I know two terms but not the common difference?
A: You can calculate the common difference by subtracting an earlier term from a later term and dividing by the number of steps between them.

Q4: How do I find the sum of the first n terms?
A: The sum \( S_n \) can be calculated using \( S_n = \frac{n}{2}(2a + (n-1)d) \) or \( S_n = \frac{n}{2}(a_1 + a_n) \).

Q5: Can n be a decimal?
A: No, term positions must be positive integers (1, 2, 3,...).