That is, each number in the sequence is the Arithmetic mean of the previous two values.

Does the sequence converge? If so, what is the limit?

Hints/Solution:

Comments:Note: (3,6) converges to 5. (1,10) converges to 7.

Can a spreadsheet help?Try an Excel file.

Extensions/Variations:

Replace the recursive definition by the Geometric Mean (where both of the seed values -- end points of a segment -- are positive numbers).

Replace the recursive definition by the Harmonic Mean (where both of the seed values are positive numbers).

Replace the recursive definition by the Arithmetic Mean of THREE numbers. Explore.

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