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 to find
• \( a_1 \) — The first term in 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 finance (loan payments), physics (uniform motion), and computer science (algorithm analysis).

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Can n be a decimal?
A: No, n must be a positive integer since it represents the position in the sequence.

Q2: What if the common difference is negative?
A: The sequence will decrease by that amount each term. The calculator handles negative differences.

Q3: How is this different from geometric sequences?
A: Arithmetic sequences add a constant difference, while geometric sequences multiply by a constant ratio.

Q4: Can I find the sum of terms with this?
A: No, this calculates individual terms. For sums, you need the arithmetic series formula.

Q5: What's the maximum term number I can calculate?
A: There's no theoretical limit, but extremely large numbers may cause computational limitations.