1. What is the Nth Term?

The nth term of an arithmetic sequence is the value of the term at position n in the sequence. It allows you to find any term in the sequence without listing all previous terms.

2. How Does the Calculator Work?

The calculator uses the arithmetic sequence formula:

Where:

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

Explanation: The formula calculates the nth term by starting with the first term and adding the common difference (n-1) times.

3. Importance of Sequence Calculation

Details: Understanding sequences is fundamental in mathematics and has applications in computer science, physics, finance, and many other fields.

4. Using the Calculator

Tips: Enter the first term of your 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 is an arithmetic sequence?
A: An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant.

Q2: Can this formula be used for geometric sequences?
A: No, this calculator is specifically for arithmetic sequences. Geometric sequences use a different formula.

Q3: What if the common difference is negative?
A: The formula works the same way - the sequence will decrease by that amount each term.

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

Q5: What are some real-world applications?
A: Arithmetic sequences model situations with constant rate of change, like simple interest, linear depreciation, or regular savings.