Harmonic Progression

Question

If a, b, c are in HP, then b equals

RankGuru · Accepted Answer

1. **Relate to AP**: If $a, b, c$ are in Harmonic Progression, then their reciprocals $1/a, 1/b, 1/c$ are in Arithmetic Progression.
2. **AP Property**: In an AP, the middle term is the average of the neighbors:
   - $\frac{1}{b} = \frac{\frac{1}{a} + \frac{1}{c}}{2}$
3. **Algebraic Manipulation**:
   - $\frac{1}{b} = \frac{a+c}{2ac}$
4. **Invert**: $b = \frac{2ac}{a+c}$.
5. **Note**: This is the definition of the Harmonic Mean.

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Harmonic Progression

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