If we assume that the bearing rate, which I denoted , changes continuously, let's see how it depends on time.
Initially it is and then it grows linearly with , so at time it becomes . The actual bearing is the shaded area under the graph (e.g., when , it is just ). The triangle area is (half of a rectangle with sides and ), so the shaded area is . Therefore, the bearing at time is .
If you insist on stepwise increment to the bearing rate, then you can use the formula for the sum of arithmetic progression: when is an integer and . Then the bearing at time is .