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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 of the harmonic progression?

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 second term\'s reciprocal will be 1 + 1 = 2, so 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 of the harmonic progression?
  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 of the harmonic progression?
  • Step 1: Understand that a harmonic progression (HP) is formed from the reciprocals of an arithmetic progression (AP).
  • Step 2: Identify the first term of the HP, which is given as 1.
  • Step 3: Recognize that the corresponding arithmetic progression has a common difference of 1.
  • Step 4: The first term of the AP is the reciprocal of the first term of the HP, which is 1. So, the first term of the AP is 1.
  • Step 5: Calculate the second term of the AP by adding the common difference (1) to the first term (1): 1 + 1 = 2.
  • Step 6: The second term of the HP is the reciprocal of the second term of the AP. So, take the reciprocal of 2: 1/2.
  • Step 7: Conclude that the second term of the harmonic progression is 1/2.
  • 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 – Understanding the relationship between terms in harmonic and arithmetic progressions through their reciprocals.
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