Question

if a,b,c,d are in a continued proportion which of the following is true :

(I) b=dk^2
(ii) a=dk^2
(iii) c=dk^2
(iv) a=dk​

Answer 1

Answer:

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