If a,b,c,d are in G.P., show that `(b-c)^2 + (c-a)^2 + (d-b)^2 = (a-d)^2`

If a, b, c are in A.P., prove that : (b+c)^2-a^2, (c+a)^2-b^2, (a+b)^2-c^2 are also in A.P.

If a, b, c and d are in G.P. show that (a^2+ b^2+ c^2) (b^2 + c^2 + d^2)= ( ab + bc + cd)^2 .

If a,b,c, d are in G.P., show that : a^(2)+b^(2), b^(2)+ c^(2) and c^(2)+d^(2) are also in G.P.

If a,b,c are in AP, than show that a^(2)(b+c)+b^(2)(c+a)+c^(2)(a+b)=(2)/(9)(a+b+c)^(3) .

If a, b, c, d are in G.P, prove that (a^n + b^n), (b^n + c^n), (c^n + d^n) are in G.P.

If a,b,c,d are in G.P., prove that (a^(n) + b^(n)), (b^(n) + c^(n)), (c^(n) + d^(n)) are in G.P.

If a,b,c, d are in G.P., show that : a+b,b+ c and c+d are also in G.P.

If a,b,c are in GP, show that the equations ax^(2)+2bx+c=0 and dx^(2)+2ex+f=0 have a common root if a/d,b/e,c/f are in

If a^(-1),b^(-1),c^(-1),d^(-1) are in A.P., then show that : b=(2ac)/(a+c) and b/d=(3a-c)/(a+c) .

If a, b,c are in G.P., prove that the following are also in G.P. : a^(2),b^(2),c^(2) .