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In a harmonic progression, if the first term is 4 and the second term is 2, what

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Question: In a harmonic progression, if the first term is 4 and the second term is 2, what is the common difference of the corresponding arithmetic progression?

Options:

  1. 1
  2. 2
  3. 3
  4. 4

Correct Answer: 2

Solution: 

The reciprocals of the terms are 1/4 and 1/2. The common difference is 1/2 - 1/4 = 1/4.

In a harmonic progression, if the first term is 4 and the second term is 2, what

Practice Questions

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

Questions & Step-by-Step Solutions

In a harmonic progression, if the first term is 4 and the second term is 2, what is the common difference of the corresponding arithmetic progression?
  • Step 1: Identify the first term of the harmonic progression, which is given as 4.
  • Step 2: Identify the second term of the harmonic progression, which is given as 2.
  • Step 3: Find the reciprocals of the terms. The reciprocal of 4 is 1/4 and the reciprocal of 2 is 1/2.
  • Step 4: Calculate the common difference of the corresponding arithmetic progression by subtracting the first reciprocal from the second reciprocal: 1/2 - 1/4.
  • Step 5: Simplify the subtraction: 1/2 is equivalent to 2/4, so 2/4 - 1/4 = 1/4.
  • Step 6: Conclude that the common difference of the corresponding arithmetic progression is 1/4.
  • 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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