If `(a-x)/(p x)=(a-y)/(q y)=(a-z)/ra n dp ,q ,a n dr` are in A.P., then prove that `x ,y ,z` are in H.P.

Suppose a is a fixed real number such that (a - x)/(px) = (a - y)/(qy) = (a - z)/(rz) If p,q,r, are in A.P., then prove that x,y,z are in H.P.

Suppose a' is a fixed real number such that (a-x)/(px)=(a-y)/(qy)=(a-z)/(rz) if p,q,r are in AP then x,y,z all are in

Let a(a!=0) is a fixed real number and (a-x)/(px)=(a-y)/(qy)=(a-z)/(rz). If p,q,r are in A.P.show that (1)/(x),(1)/(y),(1)/(z) are in A.P.

If y-z,2(y-a),y-x are in H.P. prove that x-a,y-a,z-a are in G.P.

If reciprocals of (y-x),2(y-a),(y-z) are in A.P then prove that x-a, y-a, z-a are in G.P

If reciprocals of (y-x),2(y-a), (y-z) are in A.P., prove that x-a,y-a,z-a are in G.P.

If reciprocals of (x+y)/2,y, (y+z)/2 are in A.P., show that x,y,z are in G.P.

a,b,x are in A.P.,a,b,y are in G.P. and a,b,z are in H.P. then:

STATEMENT-1 : If log (x + z) + log (x -2y +z) = 2 log (x -z) then x,v,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.