n : 1 2 3 4 5 6 7 8 9 10
Last digit of : 3 9 7 1 3 9 7 1 3 9
Last digit of : 4 6 4 6 4 6 4 6 4 6
The last digits of the number form a periodical sequence.
The period starts from n= 1 and has the length of 4.
2018 = 504*4 + 2.
So the number has the last digit 9: the second digit in the cycle.
The last digits of the number form a periodical sequence.
The period starts from n= 1 and has the length of 2.
2018 = 1008*2 + 2.
So the number has the last digit 6: the second digit in the cycle.
Therefore, the sum + has the last digit 9 + 6 = 5 (mod 10). ANSWER
