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Which of the following statements about harmonic progression is true?

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Question: Which of the following statements about harmonic progression is true?

Options:

  1. The sum of the terms is always positive.
  2. The terms can be negative.
  3. The terms are always integers.
  4. The common difference is always positive.

Correct Answer: The terms can be negative.

Solution: 

In a harmonic progression, the terms can be negative as long as their reciprocals form an arithmetic progression.

Which of the following statements about harmonic progression is true?

Practice Questions

Q1
Which of the following statements about harmonic progression is true?
  1. The sum of the terms is always positive.
  2. The terms can be negative.
  3. The terms are always integers.
  4. The common difference is always positive.

Questions & Step-by-Step Solutions

Which of the following statements about harmonic progression is true?
  • 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 an arithmetic progression is a sequence where the difference between consecutive terms is constant.
  • Step 3: Recognize that in a harmonic progression, the terms can be negative. For example, if the terms are -1, -1/2, -1/3, their reciprocals (which are -1, -2, -3) form an arithmetic progression.
  • Step 4: Conclude that the statement about harmonic progression being able to have negative terms is true, as long as their reciprocals form an arithmetic progression.
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