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,b,c are in AP and p is the AM between a and b and q is the AM between b and c, then show that b is the AM between p and q.

Let a,b,c be in A.P. If p is the A.M. between a and b and q is the A.M between b and c, then b is equal to

a , b , c , d are in increasing G.P. If the AM between a and b is 6 and the AM between c and d is 54 , then the AM of a and d is

If a^x=b^y=c^z and a,b,c are in G.P. show that 1/x,1/y,1/z are in A.P.

If a, b, c are in A.P, then show that: b+c-a ,\ c+a-b ,\ a+b-c are in A.P.

If P is the pole of chord AB of a parabola dnt he length of perpendiculars from A, P, B on any tangent to the curve be p_1, p_2 and p_3 , then (A) p_3 is the G.M. between P_1 and p_2 (B) p_3 is the A.M. between p_1 and p_2 (C) p_1 is the G.M. between P_1 and p_3 (D) none of these

If a is the A.M. of b and c and the two geometric means are G_1 and G_2 , then prove that G1^3+G2^3=2a b c

if the A.M. between pth and qth terms of an A.P. be equal to the A.M. between rth and sth terms of the A.P., then show that p+q=r+s

if the A.M. between pth and qth terms of an A.P. be equal to the A.M. between rth and sth terms of the A.P., then show that p+q=r+s

Let a,b,c are the A.M. between two numbers such that a+b+c=15 and p,q,r be the H.M. between same numbers such that 1/p+1/q+1/r=5/3 , then the numbers are