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In a harmonic progression, if the first term is 3 and the second term is 6, what

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Question: In a harmonic progression, if the first term is 3 and the second term is 6, 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 first two terms are 1/3 and 1/6. The common difference is 1/6 - 1/3 = -1/6, which is incorrect. The correct common difference is 1/3 - 1/6 = 1/6.

In a harmonic progression, if the first term is 3 and the second term is 6, what

Practice Questions

Q1
In a harmonic progression, if the first term is 3 and the second term is 6, 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 3 and the second term is 6, what is the common difference of the corresponding arithmetic progression?
  • Step 1: Identify the first term of the harmonic progression, which is 3.
  • Step 2: Identify the second term of the harmonic progression, which is 6.
  • Step 3: Find the reciprocals of the first and second terms. The reciprocal of 3 is 1/3, and the reciprocal of 6 is 1/6.
  • Step 4: Calculate the common difference of the corresponding arithmetic progression by subtracting the first reciprocal from the second reciprocal: 1/6 - 1/3.
  • Step 5: To subtract, convert 1/3 to a fraction with a common denominator of 6. This gives us 1/3 = 2/6.
  • Step 6: Now, subtract: 1/6 - 2/6 = -1/6. This is incorrect for finding the common difference.
  • Step 7: The correct way to find the common difference is to subtract the second reciprocal from the first reciprocal: 1/3 - 1/6.
  • Step 8: Again, convert 1/6 to a fraction with a common denominator of 6, which is already 1/6.
  • Step 9: Now, subtract: 1/3 (which is 2/6) - 1/6 = 2/6 - 1/6 = 1/6.
  • Step 10: Therefore, the common difference of the corresponding arithmetic progression is 1/6.
  • 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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