For the sequence {An}, if there is a constant t, for any integer n >；; N, so that it holds for any positive integer (Ai=A(i+T)), then the sequence {An} is a periodic sequence with a period of t from the nth term. If N= 1, the sequence {An} is called a pure periodic sequence; If n >；; 2, the sequence {An} is called mixed periodic sequence, and the minimum value of t is called minimum positive period, which is called period for short.

Let {An} be an integer and m be a positive integer greater than 1. If Bn is the remainder of an divided by m, that is, Bn=An(mod m) and Bn is {0, 1, 2, ..., m- 1}, then the sequence {Bn} is called {

If the module sequence {An(mod m)} is periodic, it is said that {An} is a periodic sequence about the module m.

(1) periodic sequence is an infinite sequence, and its range is a finite set;

(2) The periodic sequence must have a minimum positive period (different from the periodic function);

(3) If t is the period of the sequence {An}, it is also an arbitrary period of the sequence {An};

(4) If t is the smallest positive period of the sequence {An} and m is any period of the sequence {An}, there must be T|M, that is, m = ();

(5) It is known that the sequence {An} satisfies An+t=An(t is a constant), and Sn and Tn are the sum and product of the previous segment of {An} respectively. If n = Qt+r, 0 ≤ R.

(6) Let the series {An} be an integer series and a natural number greater than 1. If it is the remainder after division, that is, sum, it is said that the series is a modular series about {An}, which is recorded as. If the module sequence is periodic, it is said that {An} is a periodic sequence about modules.

(7) Homogeneous linear recursive sequences of any order are periodic sequences.

Knowing what a periodic sequence is and its properties, it is not difficult to get the answer to the photo.