1. What is the Arithmetic Sequence Formula?

The arithmetic sequence formula calculates the nth term of a sequence where each term increases by a constant difference. It's fundamental in algebra and has applications in finance, physics, and computer science.

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 the sequence by starting with the first term and adding the common difference multiplied by one less than the term number.

3. Importance of Arithmetic Sequences

Details: Arithmetic sequences model linear growth patterns and are used in calculating loan payments, predicting inventory needs, analyzing time series data, and solving various mathematical problems.

4. Using the Calculator

Tips: Enter the first term of the sequence, the common difference between terms, and the term number you want to find. All values must be valid numbers (n must be a positive integer).

5. Frequently Asked Questions (FAQ)

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

Q2: Can the common difference be negative?
A: Yes, a negative common difference means the sequence is decreasing.

Q3: How do I find the sum of the first n terms?
A: Use the formula Sₙ = n/2 × (2a₁ + (n-1)d) or Sₙ = n/2 × (a₁ + aₙ).

Q4: What if I know two terms but not the difference?
A: You can calculate d = (aₙ - aₘ)/(n - m) for any two terms aₙ and aₘ.

Q5: Are there real-world applications of this formula?
A: Yes, including calculating seat rows in theaters, predicting savings account growth, and scheduling payments.