If a,b,c are in G.P and `a^((1)/(x))=b^((1)/(y))=c^((1)/(z))`, prove that x,y,z are in A.P.

x+y+z = 15 if 9, x,y,z,a are in A.P., while (1)/( x) + ( 1)/( y) + ( 1)/( z) = ( 5)?( 3) if 9, x,y,z,a are in H.P., then the value of a will be :

If a^(x) = b^(y) = c^(z) and a,b,c are in G.P. , then x,y,z are in :

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 GP.

If a(1/b+1/c),b(1/c+1/a),c(1/a+1/b) are in A.P., prove that a,b,c are in A.P.

If x,y,z are in A.P. and tan^(-1)x , tan^(-1)y and tan^(-1) z are also in A.P., then :

If x,y,z are in A.P. and tan^(-1) x , tan^(-1) y and tan^(-1) z are also in A.P. then :

a^(x) = b^(y) = c^(z) = d^(t) and a,b,c,d are in G.P. , then x,y,z,t are in :

If x gt 1 , y gt 1 , z gt 1 are in G.P. , then (1)/(1 + log x) , (1)/(1 + log y) and (1)/(1 + log z) are in

If x gt 1, y gt 1 , z gt 1 are in G.P., then : ( 1)/( 1+ log x ) , ( 1)/( 1+ log y ) , ( 1) /( 1 + log z ) are in :

If a, b, c be in A.P, then a x+b y+c=0 represents