2008 AMC 12B Problem 12

For each positive integer n, the mean of the first n terms of a sequence is n. What is the 2008th term of the sequence?

\textbf{(A)}\ 2008 \qquad \textbf{(B)}\ 4015 \qquad \textbf{(C)}\ 4016 \qquad \textbf{(D)}\ 4030056 \qquad \textbf{(E)}\ 4032064

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.