1. What is an Arithmetic Sequence?

An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. The sum of the first n terms can be calculated using the formula:

where \( S_n \) is the sum, \( n \) is the number of terms, \( a \) is the first term, and \( l \) is the last term.

2. How Does the Calculator Work?

The calculator uses the arithmetic sequence sum formula:

Where:

• \( n \) — Number of terms in the sequence
• \( a \) — First term of the sequence
• \( l \) — Last term of the sequence

Explanation: The formula calculates the average of the first and last term, then multiplies by the number of terms.

3. Importance of Arithmetic Sequences

Details: Arithmetic sequences are fundamental in mathematics and appear in various real-world applications including finance, physics, and computer science.

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 and show step-by-step solution.

5. Frequently Asked Questions (FAQ)

Q1: Can I use this for decreasing sequences?
A: Yes, the formula works for both increasing and decreasing arithmetic sequences.

Q2: What if I know the common difference instead of last term?
A: You can calculate the last term using \( l = a + (n-1)d \) where \( d \) is the common difference.

Q3: What are common applications of arithmetic sequences?
A: Used in loan calculations, depreciation schedules, and simple interest problems.

Q4: How accurate is the calculator?
A: It provides precise calculations based on your input values.

Q5: Can I calculate partial sums?
A: Yes, just enter the number of terms you want to sum.