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

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

Options:

Correct Answer: 1/a, 1/b, 1/c are in AP

Solution:

In a harmonic progression, the reciprocals of the terms are in arithmetic progression, hence 1/a, 1/b, 1/c are in AP.

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

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

Step 1: Understand what a harmonic progression (HP) is. In HP, the terms are such that their reciprocals form an arithmetic progression (AP).
Step 2: Identify the first three terms of the harmonic progression, which are given as a, b, and c.
Step 3: Write down the reciprocals of these terms: 1/a, 1/b, and 1/c.
Step 4: Recall that for numbers to be in arithmetic progression, the difference between consecutive terms must be constant. This means that (1/b - 1/a) should equal (1/c - 1/b).
Step 5: Set up the equation: 1/b - 1/a = 1/c - 1/b.
Step 6: Simplify the equation to check if it holds true, confirming that the reciprocals are indeed in arithmetic progression.

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 the properties of the sequence.