Question
Wed August 29, 2012 By:

f a,b,c are in AP and b,c,d are in GP show that a,(a-b) and(d-c) are in GP

Expert Reply
Thu August 30, 2012

a, b, c are in AP

So, 2b=a + c

b, c, d are in GP

So, b^2=ad

Multiply first equation with a and subtract it from 2nd.

b^2-2ab=ad-ac-a^2

a^2 + b^2 - 2ab=a(d-c)

Hence a, (a-b) , d-c r in G.P.

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