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The nth term of an arithmetic progression is a specific term in the sequence that follows a constant difference between consecutive terms. This calculator finds the nth term when the first term, last term, and total number of terms are known.
The calculator uses the formula:
Where:
Explanation: This formula calculates any term in an arithmetic progression when the first term, last term, and total number of terms are known.
Details: Arithmetic progressions are fundamental in mathematics and have applications in various fields including finance, physics, computer science, and engineering for modeling linear growth patterns.
Tips: Enter the first term, the index of the desired term, the last term, and the total number of terms. Ensure that the index n is between 1 and the total number of terms.
Q1: What is an arithmetic progression?
A: An arithmetic progression is a sequence of numbers where the difference between consecutive terms is constant.
Q2: When is this formula particularly useful?
A: This formula is useful when you know the first and last terms of the progression and need to find any intermediate term.
Q3: What if the total number of terms is 1?
A: If ntotal = 1, then the first and last terms are the same, and the formula becomes undefined. The calculator requires ntotal > 1.
Q4: Can this calculator handle decimal values?
A: Yes, the calculator can handle decimal values for the first term, last term, and the resulting nth term.
Q5: What are some real-world applications of arithmetic progressions?
A: Applications include calculating loan payments, predicting population growth, scheduling events, and analyzing patterns in data sequences.