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Which of the following is NOT a property of harmonic progression?

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Question: Which of the following is NOT a property of harmonic progression?

Options:

  1. The terms can be expressed as fractions.
  2. The terms can be negative.
  3. The sum of the terms is always an integer.
  4. The reciprocals form an arithmetic progression.

Correct Answer: The sum of the terms is always an integer.

Solution: 

The sum of the terms in a harmonic progression is not necessarily an integer, as the terms can be fractions.

Which of the following is NOT a property of harmonic progression?

Practice Questions

Q1
Which of the following is NOT a property of harmonic progression?
  1. The terms can be expressed as fractions.
  2. The terms can be negative.
  3. The sum of the terms is always an integer.
  4. The reciprocals form an arithmetic progression.

Questions & Step-by-Step Solutions

Which of the following is NOT a property of harmonic progression?
  • Step 1: Understand what a harmonic progression (HP) is. It is a sequence of numbers where the reciprocals of the terms form an arithmetic progression (AP).
  • Step 2: Recall that in an arithmetic progression, the difference between consecutive terms is constant.
  • Step 3: Recognize that the terms in a harmonic progression can be fractions or decimals.
  • Step 4: Identify the properties of harmonic progression. One property is that the sum of the terms does not have to be an integer.
  • Step 5: Conclude that since the terms can be fractions, the sum of the terms in a harmonic progression is not necessarily an integer.
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