MathDB

25

Part of 2001 AMC 12/AHSME

Problems(1)

Sequence including 2001

Source:

12/4/2005
Consider sequences of positive real numbers of the form x,2000,y,..., x,2000,y,..., in which every term after the first is 1 less than the product of its two immediate neighbors. For how many different values of x x does the term 2001 appear somewhere in the sequence? <spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 3<spanclass=′latex−bold′>(D)</span> 4<spanclass=′latex−bold′>(E)</span> more than 4 <span class='latex-bold'>(A)</span> \ 1 \qquad <span class='latex-bold'>(B)</span> \ 2 \qquad <span class='latex-bold'>(C)</span> \ 3 \qquad <span class='latex-bold'>(D)</span> \ 4 \qquad <span class='latex-bold'>(E)</span> \ \text{more than 4}