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Question
If a, b, c, d, e are in continued proportion, prove that: a : e = a4 : b4.
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Solution
a, b, c, d, e are in continued proportion
⇒ `a/b = b/c = c/d = d/c` = k (say)
d = ek, c = ek2, b = ek3 and a = ek4
Now L.H.S. = `a/e`
= `(ek^4)/e`
= k4
R.H.S. `a^4/b^4`
= `(ek^4)^4/(ek^3)^4`
= `(e^4k^16)/(e^4k^12)`
= k16-12
= k4
∴ L.H.S. = R.H.S.
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