Question

If a,b,c,d are in continued proportion,prove that: a:d=triplicate ratio of (a-b):(b-c)

Answer 1

As LHS=RHS, hence proved....
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Answer 2

a : d = ( (a-b):(b-c) )³  if a,b,c,d are in continued proportion

Step-by-step explanation:

a,b,c,d are in continued proportion

=> a/b  = b/c =  c/d  = k

=> a = bk

   b = ck

   c = dk

a = (ck)k = dk * k * k

=> a/d = k³

(a - b)/(b -c)  =  (bk - b)/(ck - c)

= b(k -1)/c(k - 1)

= b/c

= k

= a/d = ((a - b)/(b -c))³

a : d = ( (a-b):(b-c) )³

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