IF a,b,c are unequal numbers such that a,b,c are in A.P and b-a,c-b,a are in G.P. then a:b:c=?

A.1:2:3

B.1:3:5

C.2:3:4

D.1:2:4

EXPLAIN ME DETAILLY

Given that a,b,c are in AP

let b = a + d and c = b + d

d is the common difference

then

b - a = c - b = d

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(b - a), (c - b), and a are in GP

(c - b) / ( b - a) = a / (c - b) = common ratio

(c - b)² = a(b - a)

d² = ad

a = d

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Therefore

b = a + d = 2d

c = b + d = 3d

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a:b:c = 1:2:3

Answer A