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  • Fill in the blanks For a, b, c to be in G.P. the value of aminusbbybminusc is equal to ..........

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For a, b, c to be in G.P. the value of \frac{a-b}{b-c} is equal to ..........

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It is given that a, b, c are in G.P

\\ \frac{b}{a}=\frac{c}{b}=r \\\\ \frac{a-b}{b-c}=\frac{\frac{a-b}{b}}{\frac{b-c}{b}}=\frac{\frac{a}{b}-1}{1-\frac{c}{b}}=\frac{\frac{1}{r}-1}{1-r}=\frac{\frac{1-r}{r}}{1-r} \\\\ =\frac{1}{r}=\frac{a}{b}=\frac{b}{c} \\\\

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