1. What is the Arithmetic Series Sum Formula?

The arithmetic series sum formula calculates the total of all terms in an arithmetic sequence (a sequence where each term after the first is obtained by adding a constant difference to the preceding term).

2. How Does the Calculator Work?

The calculator uses the arithmetic series sum formula:

Where:

• \( S \) — Sum of the series
• \( n \) — Number of terms in the series
• \( first \) — First term in the series
• \( last \) — Last term in the series

Explanation: The formula works by taking the average of the first and last terms, then multiplying by the number of terms.

3. Importance of Series Sum Calculation

Details: Calculating the sum of an arithmetic series is fundamental in mathematics, with applications in finance, physics, computer science, and engineering.

4. Using the Calculator

Tips: Enter the number of terms (must be positive integer), first term, and last term. The calculator will compute the sum of all terms in the arithmetic series.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between sequence and series?
A: A sequence is an ordered list of numbers, while a series is the sum of the terms of a sequence.

Q2: Can this formula be used for geometric series?
A: No, geometric series (where terms change by a common ratio) use a different formula: \( S = a_1 \times \frac{1-r^n}{1-r} \).

Q3: What if I know the common difference instead of last term?
A: You can calculate the last term using \( last = first + (n-1) \times d \), where d is the common difference.

Q4: Does the formula work for decreasing sequences?
A: Yes, the formula works for any arithmetic sequence, whether increasing or decreasing.

Q5: What are practical applications of arithmetic series?
A: Applications include calculating loan payments, total distance traveled with constant acceleration, and summing rows in computer algorithms.