1. What is the Arithmetic Sequence Formula?

An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. The nth term can be calculated using the formula:

2. How Does the Calculator Work?

The calculator uses the arithmetic sequence formula:

Where:

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

Explanation: The formula calculates any term in an arithmetic 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, physics, and computer science.

4. Using the Calculator

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

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 n be a decimal or fraction?
A: Typically n is a positive integer, but the formula works mathematically for any real number.

Q3: What if the common difference is negative?
A: A negative difference means the sequence is decreasing by that amount each term.

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 find missing terms?
A: This calculator finds specific terms. To find missing parameters, you'd need to rearrange the formula.