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Which of the following is a characteristic of harmonic progression?

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Question: Which of the following is a characteristic of harmonic progression?

Options:

  1. The terms are always increasing.
  2. The terms can be expressed as fractions.
  3. The terms are always integers.
  4. The common ratio is constant.

Correct Answer: The terms can be expressed as fractions.

Solution: 

Harmonic progression can include fractions, as it is defined through the reciprocals of an arithmetic progression.

Which of the following is a characteristic of harmonic progression?

Practice Questions

Q1
Which of the following is a characteristic of harmonic progression?
  1. The terms are always increasing.
  2. The terms can be expressed as fractions.
  3. The terms are always integers.
  4. The common ratio is constant.

Questions & Step-by-Step Solutions

Which of the following is a characteristic of harmonic progression?
  • Step 1: Understand what a harmonic progression is. It is a sequence of numbers where the reciprocals of the numbers form an arithmetic progression.
  • Step 2: Recall what an arithmetic progression is. It is a sequence of numbers where the difference between consecutive terms is constant.
  • Step 3: Recognize that since harmonic progression is based on reciprocals, it can include fractions. For example, if you have an arithmetic progression like 1, 2, 3, the reciprocals are 1, 1/2, 1/3, which are fractions.
  • Step 4: Conclude that a characteristic of harmonic progression is that it can include fractions.
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