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In a harmonic progression, if the first term is 4 and the second term is 8, what

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Question: In a harmonic progression, if the first term is 4 and the second term is 8, 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 are 1/4 and 1/8. The common difference is 1/8 - 1/4 = -1/8, which means the common difference of the corresponding arithmetic progression is 1/8.

In a harmonic progression, if the first term is 4 and the second term is 8, what

Practice Questions

Q1
In a harmonic progression, if the first term is 4 and the second term is 8, 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 8, what is the common difference of the corresponding arithmetic progression?
  • Step 1: Understand that a harmonic progression (HP) is related to an arithmetic progression (AP) through their reciprocals.
  • Step 2: Identify the first term of the HP, which is given as 4. The reciprocal of 4 is 1/4.
  • Step 3: Identify the second term of the HP, which is given as 8. The reciprocal of 8 is 1/8.
  • Step 4: Write down the reciprocals: the first term is 1/4 and the second term is 1/8.
  • Step 5: Calculate the common difference of the corresponding arithmetic progression by subtracting the first reciprocal from the second reciprocal: 1/8 - 1/4.
  • Step 6: To subtract, convert 1/4 to have a common denominator with 1/8. The common denominator is 8, so 1/4 becomes 2/8.
  • Step 7: Now perform the subtraction: 1/8 - 2/8 = -1/8.
  • Step 8: The common difference of the corresponding arithmetic progression is -1/8.
  • 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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