If a, b, c are in harmonic progression,then f | vedclass

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(C) If $a, b, c$ are in harmonic progression $(HP)$,then their reciprocals $\frac{1}{a}, \frac{1}{b}, \frac{1}{c}$ are in arithmetic progression $(AP)

Vedclass · Accepted Answer

$a/c$

Vedclass · Answer

(C) If $a, b, c$ are in harmonic progression $(HP)$,then their reciprocals $\frac{1}{a}, \frac{1}{b}, \frac{1}{c}$ are in arithmetic progression $(AP)$.Since they are in $AP$,the common difference is constant:$\frac{1}{b} - \frac{1}{a} = \frac{1}{c} - \frac{1}{b}$$\frac{a-b}{ab} = \frac{b-c}{bc}$Dividing both sides by $(b-c)$ and multiplying by $ab$,we get:$\frac{a-b}{b-c} = \frac{ab}{bc} = \frac{a}{c}$

If $a, b, c$ are in harmonic progression,then $\frac{a-b}{b-c} = \dots$

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