If `x ,y ,z` are in A.P. and `A_1` is the A.M. of `xa n dya n dA_2` is the A.M. of `ya n dz` , then prove that the A.M. of `A_1a n dA_2i sy` .

If x,y,z be three numbers in G.P. such that 4 is the A.M. between x and y and 9 is the H.M. between y and z , then y is

If a ,a_1, a_2, a_3, a_(2n),b are in A.P. and a ,g_1,g_2,g_3, ,g_(2n),b . are in G.P. and h s the H.M. of aa n db , then prove that (a_1+a_(2n))/(g_1g_(2n))+(a_2+a_(2n-1))/(g_1g_(2n-1))++(a_n+a_(n+1))/(g_ng_(n+1))=(2n)/h

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 ,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.

Find the A.M. between: 12\ a n d-8

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 is the A.M. between b and c, b the G.M. between a and c, then show that 1/a,1/c,1/b are in A.P.

Find the A.M. between: (x-y)a n d\ (x+y)

If in an A.P. the sum of m terms is equal to n and the sum of n terms is equal to m then prove that the sum of (m+n) terms is -(m+n)

If in an A.P. the sum of m terms is equal of n and the sum of n terms is equal to m , then prove that the sum of -(m+n) terms is (m+n) .