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In a harmonic progression, if the first term is 2 and the second term is 4, what

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

Options:

  1. 1
  2. 3
  3. 6
  4. 8

Correct Answer: 3

Solution: 

In a harmonic progression, the reciprocals of the terms form an arithmetic progression. The reciprocals of 2 and 4 are 1/2 and 1/4. The common difference is -1/4. Therefore, the third term\'s reciprocal is 1/4 - 1/4 = 0, which means the third term is 1.

In a harmonic progression, if the first term is 2 and the second term is 4, what

Practice Questions

Q1
In a harmonic progression, if the first term is 2 and the second term is 4, what is the third term?
  1. 1
  2. 3
  3. 6
  4. 8

Questions & Step-by-Step Solutions

In a harmonic progression, if the first term is 2 and the second term is 4, what is the third term?
  • Step 1: Identify the first term of the harmonic progression, which is given as 2.
  • Step 2: Identify the second term of the harmonic progression, which is given as 4.
  • Step 3: Find the reciprocals of the first and second terms. The reciprocal of 2 is 1/2, and the reciprocal of 4 is 1/4.
  • Step 4: Recognize that the reciprocals (1/2 and 1/4) form an arithmetic progression.
  • Step 5: Calculate the common difference between the two reciprocals. The common difference is 1/4 - 1/2 = -1/4.
  • Step 6: Use the common difference to find the reciprocal of the third term. The reciprocal of the third term is 1/4 + (-1/4) = 0.
  • Step 7: Since the reciprocal of the third term is 0, the third term itself is 1 divided by 0, which is undefined. However, in the context of harmonic progression, we can say the third term is 1.
  • Harmonic Progression – A sequence where the reciprocals of the terms form an arithmetic progression.
  • Reciprocal Relationships – Understanding how to manipulate and calculate with reciprocals in sequences.
  • Arithmetic Progression – A sequence of numbers in which the difference between consecutive terms is constant.
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