1. What is an Arithmetic Sequence?

An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. This calculator finds any term in an arithmetic sequence given the first term and common difference.

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: Each term in the sequence is found by adding the common difference to the previous term.

3. Importance of Sequence Calculation

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

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 (n). All values must be valid numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between arithmetic and geometric sequences?
A: Arithmetic sequences add a constant difference each time, while geometric sequences multiply by a constant ratio.

Q2: Can n be a decimal or fraction?
A: While mathematically possible, n typically represents whole number term positions in standard sequences.

Q3: What if my sequence isn't arithmetic?
A: This calculator only works for arithmetic sequences. Other sequence types require different formulas.

Q4: Can I calculate the sum of terms with this?
A: No, this calculates individual terms. The sum of terms requires a different formula.

Q5: What are some real-world examples of arithmetic sequences?
A: Weekly savings with constant deposits, staircase steps, evenly spaced fence posts, etc.