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

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Question: In a harmonic progression, if the first term is a and the second term is b, what is the formula for the nth term?

Options:

  1. 1/(1/n + 1/a)
  2. 1/(1/n + 1/b)
  3. 1/(1/a + 1/b)
  4. 1/(1/a - 1/b)

Correct Answer: 1/(1/n + 1/a)

Solution: 

The nth term of a harmonic progression can be expressed as 1/(1/a + (n-1)d) where d is the common difference of the corresponding arithmetic progression.

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

Practice Questions

Q1
In a harmonic progression, if the first term is a and the second term is b, what is the formula for the nth term?
  1. 1/(1/n + 1/a)
  2. 1/(1/n + 1/b)
  3. 1/(1/a + 1/b)
  4. 1/(1/a - 1/b)

Questions & Step-by-Step Solutions

In a harmonic progression, if the first term is a and the second term is b, what is the formula for the nth term?
  • Step 1: Understand that a harmonic progression (HP) is a sequence of numbers where the reciprocals of the terms form an arithmetic progression (AP).
  • Step 2: Identify the first term of the HP as 'a' and the second term as 'b'.
  • Step 3: Find the reciprocals of the first two terms: 1/a and 1/b.
  • Step 4: Calculate the common difference 'd' of the corresponding arithmetic progression (AP) using the formula: d = (1/b) - (1/a).
  • Step 5: The nth term of the HP can be expressed in terms of the first term and the common difference: nth term = 1/(1/a + (n-1)d).
  • Step 6: Substitute 'd' into the formula to get the final expression for the nth term of the harmonic progression.
  • Harmonic Progression – A sequence of numbers is in harmonic progression if the reciprocals of the terms form an arithmetic progression.
  • Common Difference – In the context of harmonic progression, the common difference refers to the difference between consecutive terms in the corresponding arithmetic progression.
  • Nth Term Formula – The formula for the nth term in a harmonic progression is derived from the relationship between harmonic and arithmetic progressions.
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