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If the first term of a harmonic progression is 1 and the common difference of th

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Question: If the first term of a harmonic progression is 1 and the common difference of the corresponding arithmetic progression is 1, what is the second term?

Options:

  1. 1/2
  2. 1/3
  3. 1/4
  4. 1/5

Correct Answer: 1/2

Solution: 

The first term is 1, and the reciprocal of the second term in HP is 1 + 1 = 2. Therefore, the second term is 1/2.

If the first term of a harmonic progression is 1 and the common difference of th

Practice Questions

Q1
If the first term of a harmonic progression is 1 and the common difference of the corresponding arithmetic progression is 1, what is the second term?
  1. 1/2
  2. 1/3
  3. 1/4
  4. 1/5

Questions & Step-by-Step Solutions

If the first term of a harmonic progression is 1 and the common difference of the corresponding arithmetic progression is 1, what is the second term?
  • Step 1: Understand that a harmonic progression (HP) is formed by taking the reciprocals of the terms of an arithmetic progression (AP).
  • Step 2: The first term of the HP is given as 1. This means the first term of the corresponding AP is 1 (since 1 is the reciprocal of 1).
  • Step 3: The common difference of the AP is given as 1. This means each term in the AP increases by 1 from the previous term.
  • Step 4: Calculate the second term of the AP. Since the first term is 1 and the common difference is 1, the second term of the AP is 1 + 1 = 2.
  • Step 5: The second term of the HP is the reciprocal of the second term of the AP. Therefore, the second term of the HP is 1 / 2.
  • Step 6: Conclude that the second term of the harmonic progression is 1/2.
  • Harmonic Progression (HP) – A sequence of numbers is in harmonic progression if the reciprocals of the terms form an arithmetic progression.
  • Arithmetic Progression (AP) – A sequence of numbers is in arithmetic progression if the difference between consecutive terms is constant.
  • Reciprocal Relationship – In a harmonic progression, the terms are related to the arithmetic progression through their reciprocals.
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