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If the first term of a harmonic progression is 3 and the second term is 6, what

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Question: If the first term of a harmonic progression 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 are 1/3 and 1/6. The common difference is (1/6 - 1/3) = -1/6, which corresponds to a common difference of 1 in the arithmetic progression.

If the first term of a harmonic progression is 3 and the second term is 6, what

Practice Questions

Q1
If the first term of a harmonic progression 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

If the first term of a harmonic progression 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 (HP), which is given as 3.
  • Step 2: Identify the second term of the harmonic progression (HP), which is given as 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 (AP) by subtracting the first reciprocal from the second reciprocal: 1/6 - 1/3.
  • Step 5: To perform the subtraction, 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.
  • Step 7: The common difference of the 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.
  • Reciprocal Relationships – Understanding how to convert between harmonic and arithmetic progressions using reciprocals.
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