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# This is an arithmetic progression with a 1 and

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Unformatted text preview: ,000 P30 = (1.11)30 10,000 = \$228,992.97 Special Integer Sequences ༉  Given a few terms of a sequence, try to identify the sequence, i.e., obtain a formula or a recurrence relation. ༉  Some questions to ask? ༉  Are there repeated terms of the same value? ༉  Can you obtain a term from the previous term by adding an amount or multiplying by an amount? ༉  Can you obtain a term by combining the previous terms in some way? ༉  Are there cycles among the terms? ༉  Do the terms match those of a well known sequence? Special Integer Sequences Example 1: 1 , 1/2 , 1/4 , 1/8 , 1/16 Solution: Note that the denominators are powers of 2. The sequence with an = 1/2n is a possible match. This is a geometric progression with a = 1 and r = 1/2. Example 2: 1 , 3 , 5 , 7 , 9 Solution: Note that each term is obtained by adding 2 to the previous term. A possible formula is an = 2n + 1. This is an ari...
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