1. What is the Nth Term from End of Arithmetic Progression?

The Nth Term from End of Arithmetic Progression is the term corresponding to the index or position n from the end of the given arithmetic progression. It helps in finding specific terms when counting backwards from the last term.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( T_{n(End)} \) — Nth Term from End of Progression
• \( l \) — Last Term of Progression
• \( n \) — Index N of Progression
• \( d \) — Common Difference of Progression

Explanation: The formula calculates the nth term from the end by subtracting (n-1) times the common difference from the last term.

3. Importance of Nth Term Calculation

Details: Calculating terms from the end of an arithmetic progression is useful in various mathematical problems, sequence analysis, and pattern recognition where reverse counting is required.

4. Using the Calculator

Tips: Enter the last term of the progression, the index n (position from the end), and the common difference. All values must be valid numbers.

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 n be any positive integer?
A: Yes, n must be a positive integer representing the position from the end of the progression.

Q3: What if the common difference is negative?
A: The formula works for both positive and negative common differences, as it follows the arithmetic progression rules.

Q4: How is this different from finding the nth term from the beginning?
A: Finding from the end uses the last term as reference, while from the beginning uses the first term.

Q5: Can this formula be used for geometric progressions?
A: No, this formula is specific to arithmetic progressions. Geometric progressions have a different formula for finding terms from the end.