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If the first three terms of a harmonic progression are 1, 1/2, and 1/3, what is

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Question: If the first three terms of a harmonic progression are 1, 1/2, and 1/3, what is the common difference of the corresponding arithmetic progression?

Options:

  1. 1/6
  2. 1/3
  3. 1/2
  4. 1

Correct Answer: 1/6

Solution: 

The reciprocals are 1, 2, and 3. The common difference is 2 - 1 = 1.

If the first three terms of a harmonic progression are 1, 1/2, and 1/3, what is

Practice Questions

Q1
If the first three terms of a harmonic progression are 1, 1/2, and 1/3, what is the common difference of the corresponding arithmetic progression?
  1. 1/6
  2. 1/3
  3. 1/2
  4. 1

Questions & Step-by-Step Solutions

If the first three terms of a harmonic progression are 1, 1/2, and 1/3, what is the common difference of the corresponding arithmetic progression?
  • Step 1: Identify the first three terms of the harmonic progression, which are 1, 1/2, and 1/3.
  • Step 2: Find the reciprocals of these terms. The reciprocal of 1 is 1, the reciprocal of 1/2 is 2, and the reciprocal of 1/3 is 3.
  • Step 3: Write down the new sequence formed by the reciprocals: 1, 2, and 3.
  • Step 4: Determine the common difference in this new sequence. The common difference is found by subtracting the first term from the second term: 2 - 1 = 1.
  • Step 5: Conclude that the common difference of the corresponding arithmetic progression is 1.
  • Harmonic Progression – A sequence of numbers is in harmonic progression if the reciprocals of the numbers 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 harmonic and arithmetic progressions through their reciprocals.
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