Can a set of three numbers be in AP as well as GP? Solution If we consider a set of three numbers a, b and c which are in AP, we know that a + c =2b. Now, if they are in GP, a*c =b^2. Now we have to see if it is possible to have three numbers satisfy both the equations. If we express a as 2b - c and replace it in a*c = b^2, it gives us (2b-c)*c = b^2 => 2bc.