10 pts] A sequence over a set A (known as alphabet) is an infinite list of elements of A, a(a, a1,a2,.). The sequence a is periodic if there exists an integer T >0 so that ai = ai +T, for all i = 0, 1, 2 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 T > 0 so that Equation (1) holds for all i 2 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 every period of a is a multiple of T