1. What is the Sum of Last N Terms of Arithmetic Progression?

The Sum of Last N Terms of an Arithmetic Progression is the summation of the terms starting from the end to the nth term of a given progression. It provides the total value when adding a specific number of terms from the end of the sequence.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( S_n(End) \) — Sum of Last N Terms of Progression
• \( n \) — Index N of Progression
• \( l \) — Last Term of Progression
• \( T_n(End) \) — Nth Term from End of Progression

Explanation: The formula calculates the sum of the last n terms by taking the average of the last term and the nth term from the end, then multiplying by the number of terms.

3. Importance of Sum Calculation

Details: Calculating the sum of last N terms is important in various mathematical applications, including series analysis, financial calculations, and pattern recognition in sequences.

4. Using the Calculator

Tips: Enter the index n (must be a positive integer), the last term of the progression, and the nth term from the end. All values must be valid numerical values.

5. Frequently Asked Questions (FAQ)

Q1: What is an Arithmetic Progression?
A: An Arithmetic Progression is a sequence of numbers in which the difference between consecutive terms is constant.

Q2: Can this formula be used for any type of progression?
A: This specific formula is designed for arithmetic progressions where the difference between terms remains constant.

Q3: What if n is larger than the total number of terms?
A: The calculator requires valid input where n should not exceed the total number of terms in the progression.

Q4: Are negative values allowed for terms?
A: Yes, the formula works with both positive and negative term values, as long as they are valid numbers.

Q5: How accurate is the calculation?
A: The calculation is mathematically precise based on the input values provided.