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 a ,b ,c are in G.P. and a-b ,c-a ,a n db-c are in H.P., then prove that a+4b+c is equal to 0.

If x ,y ,a n dz are in G.P. and x+3+,y+3,a n dz+3 are in H.P., then y=2 b. y=3 c. y=1 d. y=0

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 ,ya n dz are in A.P., a x ,b y ,a n dc z in G.P. and a ,b ,c in H.P. then prove that x/z+z/x=a/c+c/a .

If a ,b ,a n dc are in A.P. p ,q ,a n dr are in H.P., and a p ,b q ,a n dc r are in G.P., then p/r+r/p is equal to a/c-c/a b. a/c+c/a c. b/q+q/b d. b/q-q/b

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

If a ,b ,a n dc be in G.P. and a+x ,b+x ,a n dc+x in H.P. then find the value of x ( a,b,c are distinct numbers) .

If x,y and z are in A.P ax,by and cz in G.P and a, b, c in H.P then prove that x/z+z/x=a/c+c/a

a ,b ,c x in R^+ such that a ,b ,a n dc are in A.P. and b ,ca n dd are in H.P., then a b=c d b. a c=b d c. b c=a d d. none of these

If a,b,c are in H.P , b,c,d are in G.P and c,d,e are in A.P. , then the value of e is