If a, b, c are in G.P. then the value of

Question:

If $a, b, c$ are in G.P. then the value of $\frac{a-b}{b-c}$ is equal to __________________

Solution:

Let a, b and c be in g.p

i.e b = ar

ar2

i. e $\frac{a-b}{b-c}=\frac{a-a r}{a r-a r^{2}}$

$=\frac{a(1-r)}{a\left(r-r^{2}\right)}$

$=\frac{1-r}{r(1-r)}$

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

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