Mrs. Johns agrees to give her son Bill an allowance of ​$0.130.13 on the first day of his​ 14-day vacation, ​$0.260.26 on the second​ day, ​$0.520.52 on the third​ day, and so on. Write an equation of a sequence whose terms correspond to​ Bill's allowance. Find the allowance Bill will receive on the last day of his vacation.