Non Collusive Cournot Duopoly model with two firms, zero costs and linear demand curve
The temporal constraints (i.e. what happens in a period) are not very clear in this question. It is likely that the good sold is not a durable good and hence there is no "leftover demand" between periods, demand is simply 'reset'.

In period 2 leftover demand appears because firm B assumes firm A will not change its production from period 1.

Then in period 3 firm A will best respond to the unchanging production of firm B from period 2.