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In a certain sequence of numbers, every entry after the first is the product of its two neighboring entries (that is, the entries immediately before and after it). If the $100$th entry is $100$ and the $200$th entry is $200$, what is the $300$th entry?

 Dec 2, 2020
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Try this crazy idea !!:

 

1, 100, 100, 1, 1/100, 1/100, 1, 100, 100, 1,1/100, 1/100, 1, 100, 100, 1, 1/100, 1/100, 1, 100, 100, 1, 1/100, 1/100, 1, 100, 100, 1,1/100, 1/100, 1, 100, 100, 1, 1/100, 1/100, 1, 100, 100, 1, 1/100, 1/100, 1, 100, 100, 1,1/100, 1/100, 1, 100, 100, 1, 1/100, 1/100, 1, 100, 100, 1, 1/100, 1/100, 1, 100, 100, 1,1/100, 1/100, 1, 100, 100, 1, 1/100, 1/100, 1, 100, 100, 1, 1/100, 1/100, 1, 100, 100, 1,1/100, 1/100, 1, 100, 100, 1, 1/100, 1/100, 1, 100, 100, 1, 1/100, 1/100, 1, 100, 100th term=100, 1, 200, 200, 1, 1/200, 1/200..........200th term=200, 1, 300, 300, 1, 1/300, 1/300, 1..............300th term =300). Simply replace ALL 100's with 200's for another 100 terms and with 300's for another 100 terms.

 Dec 2, 2020
edited by Guest  Dec 2, 2020
edited by Guest  Dec 2, 2020

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