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

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.

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

If a,b,c are in A.P., then show that (i) a^2(b+c), b^2(c+a), c^2(a+b) are also in A.P.

If a, b, c are in G.P. , then show that (i) (a^(2) - b^(2))(b^(2) + c^(2)) = (b^(2) -c^(2)) (a^(2) + b^(2)) (ii) a( b^(2) + c^(2)) = c (a^(2) + b^(2))

If a, b, c are in A.P, then show that: \ b c-a^2,\ c a-b^2,\ a b-c^2 are in A.P.

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) + d^(2)) are in G.P.

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

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

If a ,b ,c ,d are in A.P. and x , y , z are in G.P., then show that x^(b-c)doty^(c-a)dotz^(a-b)=1.