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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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