AMC 12 2010a 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 \textbf{(B)}\ 8043 \textbf{(C)}\ 8045 \textbf{(D)}\ 8047 \textbf{(E)}\ 8049