Last Term of Arithmetic Progression given Sum of Last N Terms Calculator

Formula Used:

\[ l = \frac{\frac{Sn(End)}{n} - d \cdot (1 - n)}{2} \]

Sum of Last N Terms of Progression:

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Index N of Progression:

Common Difference of Progression:

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Last Term of Progression:

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1. What is the Last Term of Arithmetic Progression?

The Last Term of Arithmetic Progression is the final term in a sequence where each term after the first is obtained by adding a constant difference to the preceding term. It represents the endpoint value of the progression sequence.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l = \frac{\frac{Sn(End)}{n} - d \cdot (1 - n)}{2} \]

Where:

\( l \) — Last Term of Progression
\( Sn(End) \) — Sum of Last N Terms of Progression
\( n \) — Index N of Progression
\( d \) — Common Difference of Progression

Explanation: This formula calculates the last term of an arithmetic progression when given the sum of the last n terms, the index n, and the common difference between consecutive terms.

3. Importance of Last Term Calculation

Details: Calculating the last term of an arithmetic progression is essential for understanding the complete sequence, determining progression boundaries, and solving various mathematical problems involving sequences and series.

4. Using the Calculator

Tips: Enter the sum of the last n terms, the index n value, and the common difference. All values must be valid positive numbers with n being a positive integer.

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 throughout the sequence.

Q2: When is this formula particularly useful?
A: This formula is useful when you know the sum of the last few terms of a progression and need to find the actual last term value.

Q3: Can this formula be used for infinite progressions?
A: No, this formula specifically calculates the last term for finite arithmetic progressions.

Q4: What if the common difference is negative?
A: The formula works for both positive and negative common differences, as it accounts for the direction of the progression.

Q5: Are there limitations to this formula?
A: The formula assumes a standard arithmetic progression and may not work for modified or non-linear progressions.