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In a harmonic progression, if the first term is 5 and the second term is 10, wha

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Question: In a harmonic progression, if the first term is 5 and the second term is 10, what is the common difference of the corresponding arithmetic progression?

Options:

  1. 1
  2. 2
  3. 3
  4. 5

Correct Answer: 2

Solution: 

The reciprocals are 1/5 and 1/10. The common difference is 1/10 - 1/5 = -1/10, which is the difference in the arithmetic progression.

In a harmonic progression, if the first term is 5 and the second term is 10, wha

Practice Questions

Q1
In a harmonic progression, if the first term is 5 and the second term is 10, what is the common difference of the corresponding arithmetic progression?
  1. 1
  2. 2
  3. 3
  4. 5

Questions & Step-by-Step Solutions

In a harmonic progression, if the first term is 5 and the second term is 10, 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 the reciprocals of its terms.
  • Step 2: Identify the first term of the HP, which is 5. The reciprocal of 5 is 1/5.
  • Step 3: Identify the second term of the HP, which is 10. The reciprocal of 10 is 1/10.
  • Step 4: Write down the reciprocals: the first term is 1/5 and the second term is 1/10.
  • Step 5: Calculate the common difference of the corresponding arithmetic progression (AP) by subtracting the first reciprocal from the second reciprocal: 1/10 - 1/5.
  • Step 6: To perform the subtraction, convert 1/5 to a fraction with a common denominator of 10: 1/5 = 2/10.
  • Step 7: Now subtract: 1/10 - 2/10 = -1/10.
  • Step 8: The result, -1/10, is the common difference of the corresponding arithmetic progression.
  • 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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