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

If a, b, c are in A.P. and a, b, c + 1 are in G.P. then prove that 4a=(a-c)^2 .

The pth, qth and rth term of a G.P. are x, y, z respectively, then prove that- x^(q-r).y^(r-p).z^(p-q)=1 .

If pth, qth and rth term of an A.P. be a,b,c then prove that. a(q-r)+b(r-p)+c(p-q)=0

The numbers x, 8, y (xney) are in G.P. and the numbers x, y,-8 are in A.P., then show that x = 16, y = 4

If a, b, c are in A.P. and a,b, d are in G.P., prove that a, a-b, d-c are in G.P.

x and y are two positive integers such that 2,x, y are in A.P. and x, y, 9 are in G.P. then show that -x= 4, y= 6.

If x, y, z,w in are in G.P., prove that (xy-wz)/(y^2-z^2)=(x+z)/y .

If pth, qth and rth term of a G.P. are in G.P. then prove that p, q, r are in A.P.

If the sums of an A.P. upto pth, qth and rth terms are a, b and c respectively, prove that- a/p(q-r)+b/q(r-p)+c/r(p-q)=0 .

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