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If the first term of a harmonic progression is 4 and the common difference of th

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Question: If the first term of a harmonic progression is 4 and the common difference of the corresponding arithmetic progression is 2, what is the second term?

Options:

  1. 2
  2. 3
  3. 4
  4. 5

Correct Answer: 5

Solution: 

The first term is 4, and the reciprocal is 1/4. The second term\'s reciprocal will be 1/4 + 2 = 9/4, so the second term is 4/9.

If the first term of a harmonic progression is 4 and the common difference of th

Practice Questions

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

Questions & Step-by-Step Solutions

If the first term of a harmonic progression is 4 and the common difference of the corresponding arithmetic progression is 2, what is the second term?
  • Step 1: Identify the first term of the harmonic progression, which is given as 4.
  • Step 2: Find the reciprocal of the first term. The reciprocal of 4 is 1/4.
  • Step 3: Identify the common difference of the corresponding arithmetic progression, which is given as 2.
  • Step 4: Add the common difference (2) to the reciprocal of the first term (1/4). This gives us: 1/4 + 2.
  • Step 5: Convert 2 into a fraction with a denominator of 4. So, 2 = 8/4.
  • Step 6: Now add the two fractions: 1/4 + 8/4 = 9/4.
  • Step 7: The second term of the harmonic progression is the reciprocal of 9/4. The reciprocal is 4/9.
  • 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 manipulate and calculate the reciprocals of terms in harmonic and arithmetic progressions.
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