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In a harmonic progression, if the first term is 1 and the second term is 1/2, wh

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Question: In a harmonic progression, if the first term is 1 and the second term is 1/2, what is the common difference of the corresponding arithmetic progression?

Options:

  1. 1/2
  2. 1/4
  3. 1/6
  4. 1/8

Correct Answer: 1/4

Solution: 

The reciprocals are 1 and 2, which are in arithmetic progression with a common difference of 1/2.

In a harmonic progression, if the first term is 1 and the second term is 1/2, wh

Practice Questions

Q1
In a harmonic progression, if the first term is 1 and the second term is 1/2, what is the common difference of the corresponding arithmetic progression?
  1. 1/2
  2. 1/4
  3. 1/6
  4. 1/8

Questions & Step-by-Step Solutions

In a harmonic progression, if the first term is 1 and the second term is 1/2, what is the common difference of the corresponding arithmetic progression?
  • Step 1: Understand that a harmonic progression (HP) is a sequence of numbers whose reciprocals form an arithmetic progression (AP).
  • Step 2: Identify the first term of the HP, which is given as 1.
  • Step 3: Identify the second term of the HP, which is given as 1/2.
  • Step 4: Find the reciprocals of the HP terms: the reciprocal of 1 is 1, and the reciprocal of 1/2 is 2.
  • Step 5: Now we have the first two terms of the corresponding AP: 1 and 2.
  • Step 6: Calculate the common difference of the AP by subtracting the first term from the second term: 2 - 1 = 1.
  • Step 7: Therefore, 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 terms form an arithmetic progression.
  • Arithmetic Progression – A sequence of numbers is in arithmetic progression if the difference between consecutive terms is constant.
  • Common Difference – The constant difference between consecutive terms in an arithmetic progression.
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