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 are in A.P and A_(1) is the A.M of x and y and A_(2) is the A.M of y and z then A.M of A_(1) and A_(2) is

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 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.

If a ,ba n dc are in A.P., and pa n dp ' are respectively, A.M. and G.M. between aa n dbw h i l eq , q ' are , respectively, the A.M. and G.M. between ba n dc , then p^2+q^2=p^('2)+q^('2) b. p q=p ' q ' c. p^2-q^2=p^('2)-q^('2) d. none of these

The sum of m and n terms of an A.P. are n and m respectively. Prove that the sum of (m + n) terms will be - (m+n).

In an A.P.the sum of m terms of an AP is n and sum of n terms of AP is m,then prove that sum of (m+n) terms of AP is -(m+n)

in figure,M is the mid-point of AB and N is the mid-point of BC(1) if AB=BC, prove that AM=NC

in figure,M is the mid-point of AB and N is the mid-point of BC(1) if AB=BC, prove that AM=NC

If the A.M. between mth and nth terms of an A.P. be equal to the A.M. between pth and qth terms of an A.P. then prove that m+n=p+q .

The A.M. between m and n and the G.M. between a and b are each equal to (ma+nb)/(m+n) . Then m=