1. What Is The Sum Of First N Terms Of Arithmetic Progression Given NthTerm?

The sum of first N terms of an arithmetic progression given the Nth term is calculated using the formula that relates the number of terms, the first term, and the Nth term to find the total sum of the sequence.

2. How Does The Calculator Work?

The calculator uses the formula:

Where:

• \( S_n \) — Sum of first N terms of progression
• \( n \) — Index N of progression
• \( a \) — First term of progression
• \( T_n \) — Nth term of progression

Explanation: This formula calculates the sum of an arithmetic progression by taking the average of the first and last terms and multiplying by the number of terms.

3. Importance Of Sum Calculation

Details: Calculating the sum of an arithmetic progression is fundamental in mathematics and has applications in various fields including finance, physics, and computer science for analyzing sequences and series.

4. Using The Calculator

Tips: Enter the index N (must be a positive integer), the first term of the progression, and the Nth term. All values must be valid numerical inputs.

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 geometric progressions?
A: No, this formula is specific to arithmetic progressions. Geometric progressions have a different sum formula.

Q3: What if the progression has negative terms?
A: The formula works for both positive and negative terms as long as the progression is arithmetic.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact for arithmetic progressions when correct values are provided.

Q5: Can I use this for non-integer values?
A: While the formula works mathematically, in practice, index N should typically be a positive integer representing the number of terms.