MathDB

31

Part of 2013 National Olympiad First Round

Problems(1)

P31 [Algebra] - Turkish NMO 1st Round - 2013

Source:

4/20/2013
Let (an)n=1∞(a_n)_{n=1}^\infty be a real sequence such that an=(n−1)a1+(n−2)a2+⋯+2an−2+an−1a_n = (n-1)a_1 + (n-2)a_2 + \dots + 2a_{n-2} + a_{n-1} for every n≥3n\geq 3. If a2011=2011a_{2011} = 2011 and a2012=2012a_{2012} = 2012, what is a2013a_{2013}?
<spanclass=′latex−bold′>(A)</span> 6025<spanclass=′latex−bold′>(B)</span> 5555<spanclass=′latex−bold′>(C)</span> 4025<spanclass=′latex−bold′>(D)</span> 3456<spanclass=′latex−bold′>(E)</span> 2013 <span class='latex-bold'>(A)</span>\ 6025 \qquad<span class='latex-bold'>(B)</span>\ 5555 \qquad<span class='latex-bold'>(C)</span>\ 4025 \qquad<span class='latex-bold'>(D)</span>\ 3456 \qquad<span class='latex-bold'>(E)</span>\ 2013