1. What is the Last Term of Arithmetic Progression Formula?

The formula calculates the last term of an arithmetic progression when the sum of all terms, the number of terms, and the first term are known. It is derived from the standard sum formula of arithmetic progression.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l \) — Last Term of Progression
• \( S_{Total} \) — Sum of Total Terms of Progression
• \( n_{Total} \) — Number of Total Terms of Progression
• \( a \) — First Term of Progression

Explanation: This formula is derived from the standard arithmetic progression sum formula \( S = \frac{n}{2} \times (a + l) \), rearranged to solve for the last term.

3. Importance of Last Term Calculation

Details: Calculating the last term of an arithmetic progression is essential in various mathematical and real-world applications, including financial calculations, physics problems, and pattern analysis in sequences.

4. Using the Calculator

Tips: Enter the sum of all terms, the total number of terms, and the first term. All values must be valid positive numbers with appropriate constraints.

5. Frequently Asked Questions (FAQ)

Q1: What is an arithmetic progression?
A: An arithmetic progression is a sequence of numbers where the difference between consecutive terms is constant.

Q2: Can this formula be used for any arithmetic progression?
A: Yes, this formula works for any arithmetic progression where the sum of terms, number of terms, and first term are known.

Q3: What if the number of terms is zero or negative?
A: The calculator requires the number of terms to be a positive integer greater than zero.

Q4: How accurate are the results?
A: The results are mathematically precise based on the input values, with rounding to four decimal places for display.

Q5: Can this calculator handle decimal values?
A: Yes, the calculator accepts decimal values for the sum and first term inputs.