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Question
If three quantities are in continued proportion, show that the ratio of the first to the third is the duplicate ratio of the first to the second.
Solution
Let x, y and z are the three quantities which are in continued proportion
Then, x : y :: y : z => y2 = xz
Now, we have to prove that
x : z = x2 : y2
⇒ xy2 = x2z
LHS
= xy2 = x(xz) = x2z = RHS
LHS = RHS
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