Harmonic Progression
If a, b, c are in HP, then b equals
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About This Question
- Subject
- mathematics
- Chapter
- sequence and series
- Topic
- harmonic progression
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
2ac/(a + c)
- Relate to AP: If a,b,c are in Harmonic Progression, then their reciprocals 1/a,1/b,1/c are in Arithmetic Progression.
- AP Property: In an AP, the middle term is the average of the neighbors:
- b1=2a1+c1
- Algebraic Manipulation:
- b1=2aca+c
- Invert: b=a+c2ac.
- Note: This is the definition of the Harmonic Mean.
This medium difficulty mathematics question is from the chapter sequence and series, covering the topic of harmonic progression. It appeared in the 2025 exam.
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