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In a harmonic progression, if the first term is 2 and the second term is 4/3, wh

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Question: In a harmonic progression, if the first term is 2 and the second term is 4/3, what is the third term?

Options:

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

Correct Answer: 3/2

Solution: 

In a harmonic progression, the reciprocals of the terms form an arithmetic progression. The reciprocals of the first two terms are 1/2 and 3/4. The common difference is 1/4, so the reciprocal of the third term is 1/2 + 1/4 = 3/4. Therefore, the third term is 1/(3/4) = 4/3.

In a harmonic progression, if the first term is 2 and the second term is 4/3, wh

Practice Questions

Q1
In a harmonic progression, if the first term is 2 and the second term is 4/3, what is the third term?
  1. 1
  2. 3/2
  3. 2/3
  4. 1/2

Questions & Step-by-Step Solutions

In a harmonic progression, if the first term is 2 and the second term is 4/3, what is the third term?
  • Step 1: Identify the first term of the harmonic progression, which is 2.
  • Step 2: Identify the second term of the harmonic progression, which is 4/3.
  • Step 3: Find the reciprocals of the first two terms. The reciprocal of 2 is 1/2, and the reciprocal of 4/3 is 3/4.
  • Step 4: Recognize that the reciprocals (1/2 and 3/4) form an arithmetic progression.
  • Step 5: Calculate the common difference between the two reciprocals. The common difference is 3/4 - 1/2 = 1/4.
  • Step 6: Add the common difference to the last reciprocal (3/4) to find the reciprocal of the third term. So, 3/4 + 1/4 = 1.
  • Step 7: The reciprocal of the third term is 1, which means the third term itself is 1/1 = 1.
  • Harmonic Progression – A sequence where the reciprocals of the terms form an arithmetic progression.
  • Arithmetic Progression – A sequence of numbers in which the difference between consecutive terms is constant.
  • Reciprocal Relationships – Understanding how to manipulate and relate terms through their reciprocals.
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