AMC 10 2008b Problem 13

For each positive integer $n$, the mean of the first $n$ terms of a sequence is $n$. What is the $2008^{\text{th}}$ term of the sequence? $\mathrm{(A)}\ {{{2008}}} \mathrm{(B)}\ {{{4015}}} \mathrm{(C)}\ {{{4016}}} \mathrm{(D)}\ {{{4,030,056}}} \mathrm{(E)}\ {{{4,032,064}}}$