The next fraction is because In other words,


The next number in the sequence is Reasoning


I believe the next few numbers are And, just for fun, the previous numbers are If we write then it appears that So, successively, we find (beginning after the originally given sequence and thus confirming the value in the hint): and so forth. As a minor (equivalent) variation, What terms precede the given ones? We have $a_0,b_0,43,108,\ldots$ so Can ...

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