29. 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.`

If a ,b ,c are in G.P. and a^(1//x)=b^(1//y)=c^(1//z), then x y z are in AP (b) GP (c) HP (d) none of these

If a,b,c,d be in G.P. and a^x=b^y=c^z=d^w , prove that 1/x,1/y,1/z,1/w are in A.P.

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

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.

STATEMENT-1 : If log (x + z) + log (x -2y +z) = 2 log (x -z) then x,y,z are in H.P. STATEMENT-2 : If p , q , r in AP and (a -x)/(px) = (a-y)/(qy) = (a-z)/(rz) , then x, y, z are in A.P. STATEMENT-3 : If (a + b)/(1 - ab), b, (b + c)/(1 - bc) are in A .P. then a, (1)/(b) , c are in H.P.

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.

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.

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., then prove that a, c, e are in G.P.

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

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.