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Problem

A second order recurrence relation is defined by $u$_n+1 = ($u$_n+$u$_n1)/2; that is, each new term is the mean of the previous two terms.

For example, when $u$₁=2 and $u$₂=5, we generate the following sequence:

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

Find the limit of the sequence for different starting values.