If a, b, c are in A.P. and also in GP., show that a = b = c.

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.

If 2, a, b, 8 are in A.P. and a, b, c are in G.P., find a, b, c.

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 a, b, c are in A.P. then show that the terms given below are also in A.P. b + c, c + a, a + b

If a, b, c are in A.P. then show that the terms given below are also in A.P. b + c - a, c + a - b, a+ b - c

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

If a, b, c are in A.P. then show that the terms given below are also in A.P. a(1/b+1/c),b(1/c+1/a),c(1/a+1/b) .

If a, b, c are in A.P. then show that the terms given below are also in A.P. (b+c)^2-a^2,(c+a)^2-b^2,(a+b)^2-c^2 .

If a, b, c are in A.P. then show that the terms given below are also in A.P. a^2(b+c),b^2(c+a),c^2(a+b),{ab+bc+cane0} .

If a, b, c are in A.P. then show that the terms given below are also in A.P. 1/(bc),1/(ca),1/(ab)