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Hence the term 4 a3 b is in the expansion the 1 1

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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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