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Unformatted text preview: Find the ±rst 40 terms of the sequence de±ned by a n = ± 1 2 a n if a n is an even number 3 a n + 1 if a n is an odd number with a 1 = 11 and then do this again with a 1 = 25 . Make a conjecture about this type of sequence. Note that we can use an Excel spreadsheet to compute a n +1 from a n with the following formula when a n is the entry in cell A 1:(We conjecture that the 421 cycle is always reached) “= IF ( MOD (A1 , 2) = 0 , A1 2 , 3A1 + 1)” n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 a n 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1 4 2 1 4 2 n 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 a n 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 a n 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 n 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 a n 8 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4...
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This homework help was uploaded on 04/08/2008 for the course MATH 182 taught by Professor Keppelmann during the Spring '08 term at Nevada.
 Spring '08
 Keppelmann

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