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Stitz-Zeager_College_Algebra_e-book

# P a ray with initial point p when two rays share a

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Unformatted text preview: This is the famous Fibonacci Sequence ) 2. Determine if the following sequences are arithmetic, geometric or neither. If arithmetic, ﬁnd the common diﬀerence d; if geometric, ﬁnd the common ratio r. (a) {3n − 5}∞ n=1 (b) an = n2 + 3n + 2, n ≥ 1 1 1 1 (c) 3 , 1 , 12 , 24 , . . . 6 (g) 0.9, 9, 90, 900, . . . (d) (h) an = 3 (e) 17, 5, −7, 19, . . . (f) 2, 22, 222, 2222, . . . ∞ 1 n−1 5 n=1 n! 2, n ≥ 0. 3. Find an explicit formula for the nth term of the following sequences. Use the formulas in Equation 9.1 as needed. 1 (d) 1, 2 , 3 , 3 (a) 3, 5, 7, 9, . . . (b) 1, (c) 1, 1 −1, 1, −8, 24 248 3, 5, 7, . . . ... (e) 1, (f) x, 11 4, 9, 3 −x , 3 4 27 , 1 16 , x5 5, ... (g) 0.9, 0.99, 0.999, 0.9999, . . . ... (h) 27, 64, 125, 216, . . . 7 −x , 7 ... (i) 1, 0, 1, 0, . . . 4. Find a sequence which is both arithmetic and geometric. (Hint: Start with an = c for all n.) 5. Show that a geometric sequence can be transformed into an arithmetic sequence by taking the natural logarithm of the terms. 6. Thomas Robert Malthus is credited with saying, “The power of population...
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