Problem in Algebra and Geometric sequence I need help on this one question which is in Algebra and on Geometric progression.
The question is as follows:
In a geometric sequence prove that:
$(b-c)^2 + (c-a)^2 + (d-b)^2 = (d-a)^2$.
Thanks,
Sudeep

Let $$\frac dc=\frac cb=\frac ba=k\implies b=ak,c=bk=ak^2,d=ck=ak^3$$
$$(b-c)^2+(c-a)^2+(d-b)^2=a^2\{(k-k^2)^2+(k^2-1)^2+(k^3-k)^2\}=a^2(k^6-2k^3+1)=\{a(1-k^3)\}^2=(a-d)^2$$ 
