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

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

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 2b = a + c.

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

If a,b,c are in G.P. then show that :sum{log_(a)((b)/(c))}^(-1)=-3{log_(b)((c)/(a))}^(-1)