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?
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.
