Unformatted text preview: the sequence is arithmetic with common diﬀerence d = 2. To see if it is
5
geometric, we compute a2 = 3 and a3 = 3 . Since these ratios are diﬀerent, we conclude the
a1
a2
sequence is not geometric.
4. We met our last sequence at the beginning of the section. Given that a2 − a1 = − 5 and
4
a3 − a2 = 15 , the sequence is not arithmetic. Computing the ﬁrst few ratios, however, gives us
8
a4
a2
3 a3
3
3
a1 = − 2 , a2 = − 2 and a3 = − 2 . Since these are the only terms given to us, we assume that
the pattern of ratios continue in this fashion and conclude that the sequence is geometric.
We are now one step away from determining an explicit formula for the sequence given in (1). We
know that it is a geometric sequence and our next result gives us the explicit formula we require. 556 Sequences and the Binomial Theorem Equation 9.1. Formulas for Arithmetic and Geometric Sequences:
• An arithmetic sequence with ﬁrst term a and common diﬀerence d is given by
an = a + (n − 1)d, n≥1 • A geometric sequence wit...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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