2002 AMC 10P Problem 5

Let (a_n)_{n \geq 1} be a sequence such that a_1 = 1 and 3a_{n+1} - 3a_n = 1 for all n \geq 1. Find a_{2002}.

\text{(A) }666 \qquad \text{(B) }667 \qquad \text{(C) }668 \qquad \text{(D) }669 \qquad \text{(E) }670

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