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Chapter 12 – Sequences and Series

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1 Chapter 12 – Sequences and Series
Section 1 – Arithmetic Sequences and Series

2 An Arithmetic Sequence
An arithmetic sequence is a sequence of numbers with a difference between consecutive terms that is a constant. This difference is called the common difference. For example: 1, 4, 7, 10,... is an arithmetic sequence with a common difference of 3

3 The nth term To find the nth term of an arithmetic sequence with a first term of a1 and a common difference of d is given by the formula: an = a1 + (n-1)d

4 Examples EX 1: Find the 47th term in the arithmetic sequence -4,-1,2,5,... EX 2: Find the first term in the arithmetic sequence for which a19 = 42 and d = -2/3

5 An Arithmetic Series An arithmetic series is the indicated sum of the terms of an arithmetic sequence. In other words, take an arithmetic sequence and add all the numbers together.

6 Sum of a Finite Arithmetic Series
The sum of the first n terms of an arithmetic series is given by the formula: Sn = (n/2)(a1 + an) Of course, to use this formula you might have to figure out the an term.

7 Example EX 3: Find the sum of the first 60 terms in the arithmetic series:

8 Assignment Chapter 12, Section 1 pgs #18-38E,51,53,55


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