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If the first term of a harmonic progression is 5 and the common difference of th

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Question: If the first term of a harmonic progression is 5 and the common difference of the corresponding arithmetic progression is 2, what is the second term of the harmonic progression?

Options:

  1. 2.5
  2. 3.33
  3. 4
  4. 6

Correct Answer: 3.33

Solution: 

The first term is 5, and the second term\'s reciprocal is 1/5 + 2 = 1/5 + 2/1 = 11/5. Therefore, the second term is 5/11, which is approximately 0.45.

If the first term of a harmonic progression is 5 and the common difference of th

Practice Questions

Q1
If the first term of a harmonic progression is 5 and the common difference of the corresponding arithmetic progression is 2, what is the second term of the harmonic progression?
  1. 2.5
  2. 3.33
  3. 4
  4. 6

Questions & Step-by-Step Solutions

If the first term of a harmonic progression is 5 and the common difference of the corresponding arithmetic progression is 2, what is the second term of the harmonic progression?
  • Step 1: Identify the first term of the harmonic progression, which is given as 5.
  • Step 2: Understand that the harmonic progression is related to an arithmetic progression. The common difference of the corresponding arithmetic progression is given as 2.
  • Step 3: The first term of the arithmetic progression (AP) is the reciprocal of the first term of the harmonic progression (HP). So, the first term of the AP is 1/5.
  • Step 4: To find the second term of the AP, add the common difference (2) to the first term of the AP: 1/5 + 2.
  • Step 5: Convert 2 into a fraction with a denominator of 5: 2 = 10/5. Now, add 1/5 + 10/5 = 11/5.
  • Step 6: The second term of the harmonic progression is the reciprocal of the second term of the arithmetic progression. So, take the reciprocal of 11/5, which is 5/11.
  • Step 7: The second term of the harmonic progression is 5/11, which is approximately 0.45.
  • Harmonic Progression – A sequence of numbers where the reciprocals 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 calculate terms based on their reciprocals.
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