abk bk1 in other words apart from the rst term in

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Unformatted text preview: h first term a and common ratio r = 0 is given by an = arn−1 , n≥1 While the formal proofs of the formulas in Equation 9.1 require the techniques set forth in Section 9.3, we attempt to motivate them here. According to Definition 9.2, given an arithmetic sequence with first term a and common difference d, the way we get from one term to the next is by adding d. Hence, the terms of the sequence are: a, a + d, a + 2d, a + 3d, . . . . We see that to reach the nth term, we add d to a exactly (n − 1) times, which is what the formula says. The derivation of the formula for geometric series follows similarly. Here, we start with a and go from one term to the next by multiplying by r. We get a, ar, ar2 , ar3 and so forth. The nth term results from multiplying a by r exactly (n − 1) times. We note here that the reason r = 0 is excluded from Equation 9.1 is to avoid an instance of 00 which is an indeterminant form.4 With Equation 9.1 in place, we finally have the tools required to find an explicit formula for the nth term of the sequen...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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