A sequence over a set A (known as alphabet) is an infinite list of elements of A, a(, a1, a2,). The sequence a is periodic if there exists an integer T0 so that a,-a;+T, for all i-0. I Such a T is called a period of the sequence a and the least such T is called the period, or sometimes the least period, of a. The sequence a is eventually periodic if there exist N 0 and 0 so that Equation (1) holds for all i N. A period (resp. the least period) of an eventually periodic sequence refers to a period (resp. least period) of the periodic part of a Consider the following 1. In the alphabet [0, 1), which of the following sequences is periodic (and what is the period) and which one is not? (0101) (0101)(0101) 2. Prove that if a is a periodic (or eventually periodic) sequence with least period T then everv period of a is a multiple of T A sequence over a set A (known as alphabet) is an infinite list of elements of A, a(, a1, a2,). The sequence a is periodic if there exists an integer T0 so that a,-a;+T, for all i-0. I Such a T is called a period of the sequence a and the least such T is called the period, or sometimes the least period, of a. The sequence a is eventually periodic if there exist N 0 and 0 so that Equation (1) holds for all i N. A period (resp. the least period) of an eventually periodic sequence refers to a period (resp. least period) of the periodic part of a Consider the following 1. In the alphabet [0, 1), which of the following sequences is periodic (and what is the period) and which one is not? (0101) (0101)(0101) 2. Prove that if a is a periodic (or eventually periodic) sequence with least period T then everv period of a is a multiple of T