Stitz-Zeager_College_Algebra_e-book

Since we know that the exponent of 3x in the rst term

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Unformatted text preview: e nth term of a given sequence, and it is only through experience gained from evaluating sequences from explicit formulas that we learn to begin to recognize number patterns. The pattern 1, 4, 9, 16, . . . is rather recognizable as the squares, so the formula an = n2 , n ≥ 1 may not be too hard to determine. With this in mind, it’s possible to see 2, 5, 10, 17, . . . as the sequence 1 + 1, 4 + 1, 9 + 1, 16 + 1, . . ., so that an = n2 + 1, n ≥ 1. Of course, since we are given only a small sample of the sequence, we shouldn’t be too disappointed to find out this isn’t the only formula which generates this sequence. 1 5 For example, consider the sequence defined by bn = − 4 n4 + 2 n3 − 31 n2 + 25 n − 5, n ≥ 1. The 4 2 reader is encouraged to verify that it also produces the terms 2, 5, 10, 17. In fact, it can be shown that given any finite sample of a sequence, there are infinitely many explicit formulas all of which generate those same finite points. This means that there will be infinitely many correct answe...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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