In a harmonic progression, if the first term is 3 and the second term is 6, what

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Question: In a harmonic progression, if the first term is 3 and the second term is 6, what is the relationship between the terms?

Options:

Correct Answer: Their reciprocals are in AP

Solution:

The reciprocals of 3 and 6 are 1/3 and 1/6, which are in arithmetic progression.

In a harmonic progression, if the first term is 3 and the second term is 6, what is the relationship between the terms?

In a harmonic progression, if the first term is 3 and the second term is 6, what is the relationship between the terms?

Step 1: Understand what a harmonic progression (HP) is. In an HP, the reciprocals of the terms form an arithmetic progression (AP).
Step 2: Identify the first term of the HP, which is given as 3.
Step 3: Identify the second term of the HP, which is given as 6.
Step 4: Calculate the reciprocals of the first and second terms. The reciprocal of 3 is 1/3, and the reciprocal of 6 is 1/6.
Step 5: Check if the reciprocals (1/3 and 1/6) are in arithmetic progression. To do this, find the difference between the two reciprocals.
Step 6: Calculate the difference: (1/6) - (1/3) = (1/6) - (2/6) = -1/6.
Step 7: Since the difference is constant, the reciprocals are in arithmetic progression, confirming that the original terms (3 and 6) are in harmonic 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 Relationship – Understanding the relationship between terms in harmonic progression through their reciprocals.