If `1/(a+b),1/(2b),1/(b+c)` are three consecutive terms of an A.P., prove that `a ,b ,c` are the three consecutive terms of a G.P.

Suppose 1/(a+b),1/(2b),1/(b+c) are three consecutive terms of an AP. Prove that a,b,c are the consecutive terms of a G.P.

If 1/(x+y),1/(2y),1/(y+z) are three consecutive terms of an A.P., prove that x, y, z are three consecutive terms of a G.P.

If (1)/(x+y), (1)/(2y) , (1)/(y+z) are the three consecutive terms of an A.P. prove that x ,y,z are the three consecutive terms of a G.P.

If a,b, and c are three consecutive terms of an A.P, prove that k^(a),k^(b) and k^(c) are three consecutive terms of a G.P. Assume k to be a non zero real number.

If a, b and c are three consecutive terms of an A.P.,prove that k^a, k^b and k^c are three consecutive terms of a G.P. Assume k to be a non-zero real number.

Suppose 1/(a+b),1/(2b),1/(b+c) are three consecutive terms of an AP. Prove that (a+b)(b+c)=b(a+2b+c)

Prove that a - 5b, a - b and a + 3b are consecutive term of an A.P.

If a, b, c are three consecutive terms of an A.P. and x, y, z are three consecutive terms of a G.P. then prove that x^(b-c)timesy^(c-a)timesz^(a-b)=1

If a, b, c are three consecutive terms of an A.P. and x,y,z are three consecutive terms of a G.P., then prove that x^(b-c) . y^(c-a).z^(a-b)=1

If a, b, c are three consecutive terms of an A.P. and x,y,z are three consecutive terms of a G.P., then the value of x^(b-c).y^(c-a).Z^(a-b) is