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

If a ,b ,c ,d are in G.P. prove that: (a^2+b^2),(b^2+c^2),(c^2+d^2) are in G.P. (a^2-b^2),(b^2-c^2),(c^2-d^2) are in G.P. 1/(a^2+b^2),1/(b^2+c^2),1/(c^2+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 are in A.P., prove that a^(3)+4b^(3)+c^(3)=3b(a^(2)+c^(2)).

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. , prove that a^2+ b^2, ab + bc, b^2 +c^2 are also 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., prove that a^(2)(b+c),b^(2)(c+a),c^(2)(a+b)" are also in A.P."

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 G.P. then prove that (a^2+a b+b^2)/(b c+c a+a b)=(b+a)/(c+b)