5. The first four members of a sequence are: $2,0,1,8$. Each subsequent member of the sequence is the unit digit of the sum of the previous four members. (e.g., the fifth member is 1). Is the 2018th member of the sequence an even or odd number? Justify your answer!
Solution. Let's write out the first 20 terms of the sequence:

$$
\text { 2,0,1,8,1,0,0,9,0,9,8,6,3,6,3,8,0,7,8,3. }
$$

It is clear that the first ten terms are in order: even, even, odd, even, odd, even, even, odd, even, odd. The next ten terms are in the same order. Since $2018=201 \cdot 10+8$, it is evident that the 2018th term is an odd number.

## VII Section