If p ,q, r are in A.P., a is G.M. between p, q and b is G.M. between q, r, then prove that `a^2, q^2, b^2` 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 A.P, b, c, d are in G.P. and 1/c,1/d,1/e are in A.P. prove that a, c, e are in G.P.

If a, b, c are in A.P., prove that : (b+c)^2-a^2, (c+a)^2-b^2, (a+b)^2-c^2 are also in A.P.

If p, q, r are in A.P. while x, y, z are in G.P., prove that x^(q-r).y^(r-p).z^(p-q) =1 .

If one G.M., G and two A.M's p and q be inserted between two given numbers, prove that G^(2)= (2p-q) (2q-p)

Find the product : (p^2 – q^2) (2p + q)

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., show that p +q= r+s.

If (p+q)^(th) term of an A.P. is m and (p-q)th term is n, then the pth term is: