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2008 PUMaC Team B10

Source:

October 4, 2019
algebra

Problem Statement

Consider the sequence s0=(1,2008)s_0 = (1, 2008). Define new sequences sis_i inductively by inserting the sum of each pair of adjacent terms in si−1s_{i-1} between them — for instance, s1=(1,2009,2008)s_1 = (1, 2009, 2008). For some n,snn, s_n has exactly one term that appears twice. Find this repeated term.
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