The sum of the first 2005 terms of the sequence 1, 2, 3, 4, 1, 2, 3, 4, . . is
(A) 5011
(B) 5110
(C) 5020
(D) 5010
(E) 501
The sequence repeats every 4 terms.

How many times will the pattern $1,2,3,4$ occur in the first 2005 terms?

Since 2005 divided by 4 gives a quotient of 501 and a remainder of 1 , then the first 2005 terms contain the pattern 1, 2, 3, 4 a total of 501 times (ending at the 2004th term).

Also, the 2005th term is a 1.

Therefore, the sum of the first 2005 terms is $501(1+2+3+4)+1=501(10)+1=5011$.

ANSWER: (A)