1. What is an Arithmetic Sequence?

An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. This calculator computes the nth term of an arithmetic sequence.

2. How Does the Calculator Work?

The calculator uses the arithmetic sequence formula:

Where:

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

3. Applications of Sequences

Details: Arithmetic sequences are used in financial calculations, computer science, physics, and many areas of mathematics.

4. Using the Calculator

Tips: Enter the first term, common difference, and term number you want to calculate. All values must be valid numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between sequence and series?
A: A sequence is an ordered list of numbers, while a series is the sum of a sequence's terms.

Q2: Can this calculator handle geometric sequences?
A: No, this is specifically for arithmetic sequences. Geometric sequences have a common ratio rather than difference.

Q3: What if the common difference is negative?
A: The calculator works fine with negative differences - the sequence will decrease rather than increase.

Q4: How can I calculate the sum of terms?
A: The sum of first n terms is given by \( S_n = \frac{n}{2}(2a_1 + (n-1)d) \).

Q5: What's the maximum term number I can calculate?
A: There's no theoretical maximum, but extremely large numbers may cause floating-point precision issues.