1. What is the Nth Term of a Sequence?

The nth term of a sequence represents a formula to find any term in the sequence based on its position. For arithmetic sequences, each term increases by a constant 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: 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 Sequence Calculation

Details: Understanding sequences is fundamental in mathematics and has applications in computer science, physics, and finance for modeling patterns and growth.

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: 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 between terms.

Q2: Can this calculator handle non-integer terms?
A: Yes, the calculator works with any real numbers for the first term and common difference.

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 only calculates individual terms. For sum of terms, you would need a different formula.

Q5: How can I find the common difference if I don't know it?
A: Subtract any term from the term that follows it in the sequence (d = a₂ - a₁).