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.

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 shown that (i) (a + b)^(2) , (b +c)^(2), (c + d)^(2) are in G.P. (ii) (1)/(a^(2) + b^(2)), (1)/(b^(2) +c^(2)), (1)/(c^(2) + a^(2)) are in G.P.

If a, b, c are in GP, prove that a^(3), b^(3), c^(3) are in GP.

If a, b, c are in A.P., prove that a^(3)+4b^(3)+c^(3)=3b(a^(2)+c^(2)).

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-b),(b-c),(c-a) are in G.P.then prove that (a+b+c)^(2)=3(ab+bc+ca)

If a,b,c are in G.P. then prove that (1)/(a+b),(1)/(2b),(1)/(b+c) are also in A.P.

If a,b,c,d………are in G.P., then show that (a+b)^2, (b+c)^2, (c+d)^2 are in G.P.

If a,b,c,d………are in G.P., then show that (a-b)^2, (b-c)^2, (c-d)^2 are in G.P.