First slide

Geometric progression

Question

$If a, b, c are in geometric progression then the value of \frac{a - b}{b - c} is$

Moderate

A

$\frac{a}{b}$
B

$\frac{a}{c}$
C

$\frac{c}{b}$
D

$\frac{b}{a}$

Solution

$\begin{array}{l} a, b, c are in G.P \\ \Rightarrow b = ar, c = br \\ \frac{a - b}{b - c} = \frac{a - b}{a r - b r} = \frac{a - b}{r (a - b)} = \frac{1}{r} \\ But r = \frac{b}{a} = \frac{c}{b} \\ \frac{a - b}{b - c} = \frac{a}{b} or \frac{b}{c} \end{array}$

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