It must be a periodic sequence, the period of constant sequence is 1, and the period of general equal sum sequence is 2.
For any positive integer n, there is an+an+1+...+an+k-1=an+1+an+2+...+an+k, so for any positive integer n, an=an+k, if this sequence has n+k terms.
1. In the following list of integers (each letter or bracket represents an integer), the sum of any three adjacent integers is 20, then x+y+z=?
x，2， （），（），（），4，（），y，（），（），z
2. There are 120 positive numbers (not necessarily integers) on the circumference. Now we know that the sum of any 35 connected numbers is 200. Prove that each of these numbers does not exceed 30. (Side note: "connected" in the title means "adjacent")
answer
Question 1
x=14,y=2,z=2
x+y+z=18
Question 2
（120,35）=5
Make five numbers into a group, and the sum of every seven groups is 200, so each group has 200/7<30
So each number does not exceed 30.
