If the first three terms of a harmonic progression are a, b, and c, which of the

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Question: If the first three terms of a harmonic progression are a, b, and c, which of the following equations holds true?

Options:

Correct Answer: 1/a + 1/b = 1/c

Solution:

In a harmonic progression, the reciprocals of the terms form an arithmetic progression, hence 1/a + 1/b = 1/c.

If the first three terms of a harmonic progression are a, b, and c, which of the following equations holds true?

If the first three terms of a harmonic progression are a, b, and c, which of the following equations holds true?

Step 1: Understand what a harmonic progression (HP) is. In an HP, the terms are related to their reciprocals.
Step 2: Write down the first three terms of the harmonic progression: a, b, and c.
Step 3: Take the reciprocals of these terms: 1/a, 1/b, and 1/c.
Step 4: Recognize that the reciprocals (1/a, 1/b, 1/c) form an arithmetic progression (AP).
Step 5: Recall the property of an arithmetic progression: the middle term is the average of the other two terms.
Step 6: Apply the property: 1/b = (1/a + 1/c) / 2.
Step 7: Rearrange this equation to find a relationship between a, b, and c: 2/b = 1/a + 1/c.
Step 8: Multiply through by 2 to simplify: 2/b = 1/a + 1/c becomes 1/a + 1/b = 1/c.

Harmonic Progression – A sequence of numbers is in harmonic progression if the reciprocals of the terms form an arithmetic progression.
Arithmetic Progression – A sequence of numbers is in arithmetic progression if the difference between consecutive terms is constant.
Reciprocal Relationships – Understanding how the reciprocals of terms relate to each other in different types of progressions.