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 (d). Each term after the first is found by adding the common difference to the previous term.

2. How Does the Calculator Work?

The calculator uses the arithmetic sequence formula:

Where:

• \( a_n \) — The nth term of the sequence
• \( a_1 \) — The first term of the sequence
• \( d \) — The common difference between terms
• \( n \) — The term number to find

Explanation: The formula calculates any term in the sequence by starting with the first term and adding the common difference multiplied by one less than the term number.

3. Importance of Arithmetic Sequences

Details: Arithmetic sequences are fundamental in mathematics and appear in many real-world applications, including financial calculations, physics problems, and computer science algorithms.

4. Using the Calculator

Tips: Enter the first term of the sequence, the common difference between terms, and the term number you want to find. All values must be valid numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between arithmetic and geometric sequences?
A: In arithmetic sequences, the difference between terms is constant (addition). In geometric sequences, the ratio between terms is constant (multiplication).

Q2: Can the common difference be negative?
A: Yes, a negative common difference means each term is smaller than the previous one.

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

Q4: How do I find the sum of the first n terms?
A: Use the formula \( S_n = \frac{n}{2}(2a_1 + (n-1)d) \) or \( S_n = \frac{n}{2}(a_1 + a_n) \).

Q5: Can this calculator handle non-integer terms?
A: Yes, the calculator works with any real numbers for the first term and common difference.