## Mean Sequence

#### 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.

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