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., 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.

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., prove that: a(b^2+c^2)=c(a^2+b^2)

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