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Recursive Sequence

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April 2, 2013
induction

Problem Statement

Let (an)n≥1(a_n)_{n\geq 1} be a sequence such that a1=1a_1=1 and 3an+1−3an=13a_{n+1}-3a_n=1 for all n≥1n\geq 1. Find a2002a_{2002}.
<spanclass=′latex−bold′>(A)</span>666<spanclass=′latex−bold′>(B)</span>667<spanclass=′latex−bold′>(C)</span>668<spanclass=′latex−bold′>(D)</span>669<spanclass=′latex−bold′>(E)</span>670<span class='latex-bold'>(A) </span>666\qquad<span class='latex-bold'>(B) </span>667\qquad<span class='latex-bold'>(C) </span>668\qquad<span class='latex-bold'>(D) </span>669\qquad<span class='latex-bold'>(E) </span>670
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