(Solution) - a A sequence an is defined recursively by the equation -(2025 Original AI-Free Solution)

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(a) A sequence {an} is defined recursively by the equation an = ½ (an?1 + an ? 2) for n > 3, where a1 and a2 can be any real numbers. Experiment with various values of a1 and a2 and use your calculator to guess the limit of the sequence.
(b) Find lim n?? an in terms of a1 and a2 by expressing an+1 ? an in terms of a2 ? a1 and summing a series.