if ‘a,b,c,d’ are in continued proportion find (a-b)³:(b-c)³
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a, b, c, d are in continued proportion
Therefore, we have
a/b = b/c = c/d = k (say)
c=dk, b=ck=dk2, a=bk=dk3
Consider,
(a-b)3 : (b-c)3
= (dk3 - dk2)3 : (dk2 - dk)3
= d3k6(k - 1) : d3k3(k - 1)
= k3
a/d = dk3/d = k3
Hence, (a-b)3 : (b-c)3 = a : d
Step-by-step explanation:
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