Question

Abcs are in gp prove that a^2 - b^2 ,b^2-c^2,c^2-d^2 are in gp

Answer 1

"(a-b)2 = a2(1 - r)2

(b-c)2 = b2(1 - r)2

(c-d)2 = c2(1 - r)2

R1= (b-c)2 / (a-b)2 = b2 / a2 = r2

R2= (c-d)2 / (b-c)2 = c2  /b2 = r2

R1 = R2 = R.R = r2

So we have (a-b)2 . (b-c)2 = R (a-b)2

(c-d)2 = R (b-c)2 which is a GP.

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Answer 2

refer to the attachment