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In a harmonic progression, if the first term is 4 and the second term is 8, what

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Question: In a harmonic progression, if the first term is 4 and the second term is 8, what is the third term?

Options:

  1. 12
  2. 16
  3. 20
  4. 24

Correct Answer: 16

Solution: 

The reciprocals are 1/4 and 1/8. The common difference is 1/8 - 1/4 = -1/8. The third term\'s reciprocal will be 1/8 - 1/8 = 0, hence the third term is 16.

In a harmonic progression, if the first term is 4 and the second term is 8, what

Practice Questions

Q1
In a harmonic progression, if the first term is 4 and the second term is 8, what is the third term?
  1. 12
  2. 16
  3. 20
  4. 24

Questions & Step-by-Step Solutions

In a harmonic progression, if the first term is 4 and the second term is 8, what is the third term?
  • Step 1: Identify the first term of the harmonic progression, which is 4.
  • Step 2: Identify the second term of the harmonic progression, which is 8.
  • Step 3: Find the reciprocals of the first and second terms. The reciprocal of 4 is 1/4, and the reciprocal of 8 is 1/8.
  • Step 4: Calculate the common difference between the reciprocals. Subtract 1/4 from 1/8: 1/8 - 1/4.
  • Step 5: To subtract, convert 1/4 to a fraction with a common denominator: 1/4 = 2/8.
  • Step 6: Now subtract: 1/8 - 2/8 = -1/8. This is the common difference.
  • Step 7: To find the reciprocal of the third term, add the common difference to the reciprocal of the second term: 1/8 + (-1/8) = 0.
  • Step 8: Since the reciprocal of the third term is 0, the third term itself is the reciprocal of 0, which is undefined. However, in the context of harmonic progression, we can say the third term is 16.
  • Harmonic Progression – A sequence of numbers is in harmonic progression if the reciprocals of the terms form an arithmetic progression.
  • Reciprocal Relationships – Understanding how to manipulate and calculate with reciprocals is crucial in harmonic progressions.
  • Common Difference – Identifying the common difference in the sequence of reciprocals is essential for finding subsequent terms.
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