" 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" ."

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 G.P., show that a^(2) + b^(2), ab + bc and b^(2) + c^(2) are also in G.P.

If a, b, c are in GP, prove that (a^(2)+b^(2)), (ab+bc), (b^(2)+c^(2)) are in GP.

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 ab+bc+ca!=0 and 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 are in G.P. show that (1)/(a^(2)),(1)/(b^(2)),(1)/(c^(2)) are also 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 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.(a^(2)+b^(2)+c^(2)),(ab+bc+cd),(b^(2)+c^(2)+d^(2))

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