Stitz-Zeager_College_Algebra_e-book

101 angles and their measure 595 know the proportion

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Unformatted text preview: mean of the term immediately preceding, ak−1 it and immediately following it, ak+1 . State and prove an analogous result for geometric sequences. 9. Discuss with your classmates how the results of this section might change if we were to examine sequences of other mathematical things like complex numbers or matrices. Find an explicit formula for the nth term of the sequence i, −1, −i, 1, i, . . .. List out the first four terms of the matrix sequences we discussed in Exercise 3 in Section 8.3. 9.1 Sequences 9.1.2 561 Answers 1. (a) (b) (c) (d) 0, 1, 3, 7 −1, −1, 1, 1 3, 8, 13, 18 5 1, 1, 3 , 5 2 2 3 (h) 12, 0.12, 0.0012, 0.000012 (i) 2, 7, 22, 67 1 1 (j) −2, − 1 , − 36 , − 720 3 1 1 (k) 117, 117 , 117, 117 4 (e) x, x , x , x 4 9 16 (l) 1, x + 1, x2 + x + 1, x3 + x2 + x + 1 (f) 0, ln(2) , ln(3) , ln(4) 2 3 4 (g) 3, 2, 1, 0 (m) 1, 1, 2, 3 (e) arithmetic, d = −12 2. (a) arithmetic, d = 3 (f) neither (b) neither (c) geometric, r = (d) geometric, r = 1 2 1 5 3. (a) an = 1 + 2n, n ≥ 1 1 (b) an = − 2 (c) an...
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