AMC 12 2002a Problem 21

Consider the sequence of numbers: $4,7,1,8,9,7,6,\dots$ For $n>2$, the $n$-th term of the sequence is the units digit of the sum of the two previous terms. Let $S_n$ denote the sum of the first $n$ terms of this sequence. The smallest value of $n$ for which $S_n>10,000$ is:

$\text{(A) }1992 \text{(B) }1999 \text{(C) }2001 \text{(D) }2002 \text{(E) }2004$