<s>[INST] At Rumsey Station, a train travels from Cityville to a nearby town. On the first day of service, $$9$$ frogs are on the train. On the second day, the conductor invites all the frogs on the first day to return, and in addition, brings $$2$$ more frogs. On the third day, all the frogs that have traveled previously are invited to return, and $$3$$ more frogs are added. This pattern of operations continues for $$10$$ days. How many frogs are on the train at the end of the tenth day?[/INST]