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प्रश्न
For a, b, c to be in G.P. the value of `(a - b)/(b - c)` is equal to ______.
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उत्तर
For a, b, c to be in G.P. the value of `(a - b)/(b - c)` is equal to `a/b` or `b/c`.
Explanation:
Since a, b and c are in G.P
∴ `b/a = c/b` = r .....(Constant)
⇒ b = ar and c = br
⇒ c = ar · r = ar2
So `(a - b)/(b - c) = (a - ar)/(ar - ar^2)`
= `(a(1 - r))/(ar(1 - r))`
= `1/r`
= `a/b`
= `b/c`
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