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Which of the following statements is true regarding harmonic progressions?

Practice Questions

Q1
Which of the following statements is true regarding harmonic progressions?
  1. The sum of the terms is always constant.
  2. The product of the terms is always constant.
  3. The reciprocals of the terms form an arithmetic progression.
  4. The terms are always integers.

Questions & Step-by-Step Solutions

Which of the following statements is true regarding harmonic progressions?
  • Step 1: Understand what a harmonic progression (HP) is. It is a sequence of numbers where the reciprocals of the terms form an arithmetic progression (AP).
  • Step 2: Recall what an arithmetic progression is. In an AP, the difference between consecutive terms is constant.
  • Step 3: If you have a harmonic progression like a, b, c, then the reciprocals are 1/a, 1/b, 1/c.
  • Step 4: Check if the reciprocals (1/a, 1/b, 1/c) form an arithmetic progression. This means that (1/b - 1/a) should equal (1/c - 1/b).
  • Step 5: Conclude that since the reciprocals of the terms in a harmonic progression do indeed form an arithmetic progression, the statement is true.
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