`If a/b=b/c=c/d`, then prove that `(b-c)^3/(c-d)^3=a/d`

If a,b,c,d are in GP then prove that a(b-c)^3=d(a-b)^3 .

If a, b, c, d are in G.P., then prove that: (b-c)^(2)+(c-a)^(2)+(d-b)^(2)=(a-d)^(2)

If a

If a, b, c, d are in GP, prove that (b-c)^(2)+(c-a)^(2)+(d-b)^(2)=(a-d)^(2) .

If a,b,c,d are in H.P.then prove that a+d>b+c

If (a)/(b)=(b)/(c)=(c)/(d), then (b^(3)+c^(3)+d^(3))/(a^(3)+b^(3)+c^(3)) will be equal to (a)/(b) b.(b)/(c) c.(c)/(d) d.(d)/(a)

If a,b,c and d are in H.P.,then prove that (b+c+d)/a,(c+d+a)/b,(d+a+b)/c and (a+b+c)/d, are in A.P.

If a,b,c,d are in G.P.then prove that (a^(3)+b^(3))^(-1),(b^(3)+c^(3))^(-1),(c^(3)+d^(3))^(-1) are also in G.P.

a=2b=3c=4d then a:b:c:d is

If a,b,c,d are in GP then prove that a+b,b+c,c+d are in GP.