If `(a-x)/(px)=(a-y)/(qy)=(a-z)/(rz)` and p,q and r are in A.P., then prove that x,y,z are in H.P.

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.

If x ,1,a n dz are in A.P. and x ,2,a n dz are in G.P., then prove that x ,a n d4,z are in H.P.

If sin(y+z-x),sin(z+x-y),"sin"(x+y-z) are in A.P., then t a n x ,tany ,tanz are in (a)A.P. (b) G.P. (c) H.P. (d) none of these

If x=Sigma_(n=0)^(oo) a^n,y=Sigma_(n=0)^(oo) b^n,z=Sigma_(n=0)^(oo) c^n where a, b,and c are in A.P and |a|lt 1 ,|b|lt 1 and |c|1 then prove that x,y and z are in H.P

Find the x, y, and z, given that the number x, 10, y, 24, z are in A.P.

If x, y, z are in A.P then e^(-x) , e^(-y) and e^(-z) are

If ("log"x)/(y - z) = ("log" y)/(z - x) = ("log" z)/(x - y) , then prove that xyz = 1.

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 the 3^(rd) , 8^(th) and 13^(th) terms of a G.P are x,y,z respectively, then prove that x,y,z are in G.p. .