1. What is the Nth Term of a Sequence?

The nth term of an arithmetic sequence is the value of the term at position n in the sequence. Arithmetic sequences have a constant difference between consecutive terms.

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, finance, and many other fields.

4. Using the Calculator

Tips: Enter the first term, common difference, and the term number you want to find. All values must be valid numbers with n ≥ 1.

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 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 the common difference is zero?
A: If d=0, all terms in the sequence will be equal to the first term.

Q4: How do I find the sum of the first n terms?
A: Use the formula Sₙ = n/2 × (2a₁ + (n-1)d) for the sum of an arithmetic sequence.

Q5: Can this calculator solve for n if I know the term value?
A: No, this calculator specifically finds the term value given n. You would need to rearrange the formula to solve for n.