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.

If a, b, c are in AP, x is the GM between a and b, y is the GM between b and c, then show that b^(2) is the AM between x^(2) and y^(2) .

a,b,c are in A.P., x is G.M between a and b, y is the G.M between b and c then b^2 is

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=

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 b 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.

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

If a,b,c are in G.P. then prove that (1)/(a+b),(1)/(2b),(1)/(b+c) are also in A.P.

If the A.M. between p^(th) and q^(th) terms of an A.P. , be equal to the A.M., between m^(th) and n^(th) terms of the A.P. , then show that p + q = m + n .