Last Term of Arithmetic Progression given Pth and Qth Terms Calculator

Formula Used:

\[ l = \frac{T_p \times (q-1) - T_q \times (p-1)}{q-p} + (n_{Total}-1) \times \frac{T_q - T_p}{q-p} \]

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 the sequence where each term differs from the previous one by a constant value called the common difference. This calculator finds the last term when given specific terms at positions p and q.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l = \frac{T_p \times (q-1) - T_q \times (p-1)}{q-p} + (n_{Total}-1) \times \frac{T_q - T_p}{q-p} \]

Where:

\( l \) — Last Term of Progression
\( T_p \) — Pth Term of Progression
\( T_q \) — Qth Term of Progression
\( p \) — Index P of Progression
\( q \) — Index Q of Progression
\( n_{Total} \) — Number of Total Terms of Progression

Explanation: The formula calculates the last term by utilizing the relationship between given terms at specific positions and the total number of terms in the arithmetic progression.

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 values of the pth term, qth term, their respective indices (p and q), and the total number of terms. Ensure that p and q are distinct positive integers and that nTotal is greater than or equal to the maximum of p and q.

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 p and q be the same?
A: No, p and q must be different indices to avoid division by zero in the formula.

Q3: What if nTotal is less than p or q?
A: The calculator requires nTotal to be at least as large as the maximum of p and q to ensure valid progression indices.

Q4: Are negative terms allowed?
A: Yes, the calculator supports both positive and negative terms in the arithmetic progression.

Q5: How accurate are the results?
A: Results are calculated with precision up to four decimal places for accurate representation.