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In a harmonic progression, if the first term is 5 and the common difference of t

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Question: In a harmonic progression, if the first term is 5 and the common difference of the corresponding arithmetic progression is 2, what is the second term?

Options:

  1. 2.5
  2. 3.33
  3. 4
  4. 6

Correct Answer: 6

Solution: 

The first term is 5, and the second term in the harmonic progression corresponds to the reciprocal of the second term in the arithmetic progression, which is 5 + 2 = 7. Thus, the second term is 1/7.

In a harmonic progression, if the first term is 5 and the common difference of t

Practice Questions

Q1
In a harmonic progression, if the first term is 5 and the common difference of the corresponding arithmetic progression is 2, what is the second term?
  1. 2.5
  2. 3.33
  3. 4
  4. 6

Questions & Step-by-Step Solutions

In a harmonic progression, if the first term is 5 and the common difference of the corresponding arithmetic progression is 2, what is the second term?
  • Step 1: Identify the first term of the harmonic progression, which is given as 5.
  • Step 2: Understand that the harmonic progression is related to an arithmetic progression (AP).
  • Step 3: The first term of the corresponding arithmetic progression (AP) is also 5.
  • Step 4: The common difference of the AP is given as 2.
  • Step 5: Calculate the second term of the AP by adding the common difference to the first term: 5 + 2 = 7.
  • Step 6: The second term of the harmonic progression corresponds to the reciprocal of the second term of the AP.
  • Step 7: Calculate the reciprocal of 7: 1/7.
  • Step 8: Conclude that the second term of the harmonic progression is 1/7.
  • 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 – The terms of a harmonic progression are the reciprocals of the terms of the corresponding arithmetic progression.
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