2010 AMC 12A Problem 10

The first four terms of an arithmetic sequence are p, 9, 3p-q, and 3p+q. What is the 2010^\text{th} term of this sequence?

\textbf{(A)}\ 8041 \qquad \textbf{(B)}\ 8043 \qquad \textbf{(C)}\ 8045 \qquad \textbf{(D)}\ 8047 \qquad \textbf{(E)}\ 8049

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