If `a ,b ,c` are in A.P. and `a^2, b^2, c^2` are in H.P., then prove that either `a=b=cora ,b ,c=c/2` form a G.P.

If a,b,c are in A.P.and a^(2),b^(2),c^(2) are in H.P. then prove that either a^(2),b^(2),c^(2) are in H.P.a=b=c or a,b,-(c)/(2) form a G.P.

If a,b,c are in A.P and a,b,d are in G.P, prove that a,a-b,d-c are in G.P.

If a, b, c are in A.P. and a, x, b, y, c are in G.P., then prove that b^(2) is the arithmatic mean of x^(2)" and "y^(2).

If a,b,c are in A.P and a^2,b^2,c^2 are in H.P then which is of the following is /are possible ?

If a,b,c are in G.P.and b-c,c-a,a-b are in H.P.then prove that a+b+c=-3(ac)^((1)/(2))

If the angles A,B,C of a triangle are in A.P. and sides a,b,c, are in G.P., then prove that a^2, b^2,c^2 are in A.P.

If 1/a,1/b,1/c are in A.P and a,b -2c, are in G.P where a,b,c are non-zero then

If a,b,c, are in A.P., b,c,d are in G.P. and c,d,e, are in H.P., then a,c,e are in