If `a,g_1,g_2,b` are in G.P., then prove that `(g_1^2)/(g_2) + (g_2^2)/(g_1)`= a+b.

If g_1 , g_2 are two G.M's between two numbers a and b, then (g_1^2)/(g_2)+(g_2^2)/(g_1) is equal to:

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 ,a_1, a_2, a_3, a_(2n),b are in A.P. and a ,g_1,g_2,g_3, ,g_(2n),b . are in G.P. and h s the H.M. of aa n db , then prove that (a_1+a_(2n))/(g_1g_(2n))+(a_2+a_(2n-1))/(g_1g_(2n-1))++(a_n+a_(n+1))/(g_ng_(n+1))=(2n)/h

If a is the A.M. of b and c and the two geometric means are G_(1) and G_(2) , then prove that G_(1)^(3)+G_(2)^(3) = 2abc

If a, b,c are in G.P., prove that the following are also in G.P. : a^(2)+b^(2),ab+bc,b^(2)+c^(2) .

If a, b,c are in G.P., prove that the following are also in G.P. : a^(2),b^(2),c^(2) .

If p ,q, r are in A.P., a is G.M. between p, q and b is G.M. between q, r, then prove that a^2, q^2, b^2 are in A.P.

If a, b,c are in G.P., prove that the following are also in G.P. : a^(3),b^(3),c^(3) .

Area of the triangle with vertices (a, b), (x_1,y_1) and (x_2, y_2) where a, x_1,x_2 are in G.P. with common ratio r and b, y_1, y_2 , are in G.P with common ratio s, is

If a, b, c are in A.P, b, c, d are in G.P. and 1/c,1/d,1/e are in A.P. prove that a, c, e are in G.P.