Last Term of Arithmetic Progression given Nth Term Calculator

Formula Used:

\[ l = a + (nTotal - 1) \times \frac{T_n - a}{n - 1} \]

Last Term of Progression (l):

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1. What is the Last Term of Arithmetic Progression?

The Last Term of an 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 termination point of the given progression sequence.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l = a + (nTotal - 1) \times \frac{T_n - a}{n - 1} \]

Where:

\( l \) — Last Term of Progression
\( a \) — First Term of Progression
\( nTotal \) — Number of Total Terms of Progression
\( T_n \) — Nth Term of Progression
\( n \) — Index N of Progression

Explanation: This formula calculates the last term of an arithmetic progression when you know the first term, total number of terms, any nth term, and its position in the sequence.

3. Importance of Last Term Calculation

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

4. Using the Calculator

Tips: Enter the first term, total number of terms, any nth term value, and its position index. Ensure all values are valid (n > 1, nTotal > 0).

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: Why do we need to calculate the last term?
A: Knowing the last term helps in understanding the complete sequence, calculating the sum of the progression, and solving various mathematical problems.

Q3: Can this formula be used for any nth term?
A: Yes, as long as you know the value of any term and its position in the sequence, you can calculate the last term.

Q4: What if the common difference is known?
A: If the common difference is known, you can use the simpler formula: l = a + (nTotal - 1) × d, where d is the common difference.

Q5: Are there limitations to this formula?
A: This formula works only for arithmetic progressions and requires that n > 1 (to avoid division by zero).