The pattern uses the logic of multiplying by increasing integers and then adding or subtracting a constant to get the next term. The sequence progresses as (15 x 1) + 1 = 16, (16 x 2) + 2 = 34, (34 x 3) + 3 = 105, and (105 x 4) + 4 = 424. The next term should be (424 x 5) + 5 = 2125, making 2124 the odd term out.