If a,b,c and d are in G.P , then show that `ax^(2)+c` divides `ax^(3)+bx^(2)+cx+d`

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

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

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

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

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

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