What is the relationship between the harmonic mean and the terms of a harmonic progression?
Practice Questions
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Q1
What is the relationship between the harmonic mean and the terms of a harmonic progression?
It is the average of the terms.
It is the reciprocal of the arithmetic mean of the reciprocals.
It is the sum of the terms.
It is the product of the terms.
The harmonic mean of a set of numbers is the reciprocal of the arithmetic mean of their reciprocals.
Questions & Step-by-step Solutions
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Q
Q: What is the relationship between the harmonic mean and the terms of a harmonic progression?
Solution: The harmonic mean of a set of numbers is the reciprocal of the arithmetic mean of their reciprocals.
Steps: 5
Step 1: Understand what a harmonic progression (HP) is. A harmonic progression is a sequence of numbers where the reciprocals of the numbers form an arithmetic progression (AP).
Step 2: Identify the terms of a harmonic progression. For example, if the terms are a, b, c, then their reciprocals are 1/a, 1/b, 1/c.
Step 3: Calculate the arithmetic mean of the reciprocals. The arithmetic mean of 1/a, 1/b, and 1/c is (1/a + 1/b + 1/c) / 3.
Step 4: Find the harmonic mean. The harmonic mean of the original terms a, b, and c is the reciprocal of the arithmetic mean calculated in Step 3.
Step 5: Conclude the relationship. The harmonic mean gives a single value that represents the central tendency of the terms in the harmonic progression.
