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Mean Sequence

Problem

A second order recurrence relation is defined by un+1 = (un+unminus1)/2; that is, each new term is the mean of the previous two terms.

For example, when u1=2 and u2=5, we generate the following sequence:

2, 5, 3.5, 4.25, 3.875, ... .

Find the limit of the sequence for different starting values.

Problem ID: 212 (06 Mar 2005)     Difficulty: 3 Star

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