Given that `x+y+z=15w h e na ,x ,y ,z ,b` are in A.P. and `1/x+1/y+1/z+=5/3w h e n a ,x ,y ,z ,b` are in H.P.

If x^2+9y^2+25 z^2=x y z((15)/x+5/y+3/z),t h e n x ,y ,a n dz are in H.P. b. 1/x ,1/y ,1/z are in A.P. c. x ,y ,z are in G.P. d. 1/a+1/d=1/b=1/c

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

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

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

The value of x + y + z is 15. If a, x, y, z, b are in AP while the value of (1)/(x) + (1)/(y) + (1)/(z) " is " (5)/(3) . If a, x, y, z b are in HP, then find a and b .

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=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