Stitz-Zeager_College_Algebra_e-book

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## 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.

Ask a homework question - tutors are online