2. Choi 2012

3. What is a Series? A series is the sum of terms of a sequence. The sum of the first n terms in a sequence is denoted as S n. S 5  the sum of the first 5 terms

4. Arithmetic Series Recall: A sequence like 2, 5, 8, 11,…, is called an arithmetic sequence with a = 2 and d = 3. Therefore a series that corresponds to this arithmetic sequence is 2 + 5 + 8 + 11 +…, is called an arithmetic series.

5. Arithmetic Series Formula The Sum of the First n terms of an Arithmetic Series Recall: Arithmetic Sequence formula Rewrite this series in reverse order Add this two rows together There are n terms in total Formula 1 or a +(n - 1)d Formula 2

6. Example 1 – Sum of a Series given the first term Find the sum of the first 60 terms of each series.

7. Example 2 – Sum of a series given first and last terms Find the sum of the arithmetic series 5 + 9 + 13 +... + 201. 50 There are 50 terms in the series. 50

8. Example 3 – Word Problem A student is offered a job with a math teacher that will last 20 hours. The first option pays $4.75 for the first hour, $5 for the second hour, $5.25 for the next hour, and so on. The second option pays $7/h for all hours worked. Which option pays more? 20 The amount earned by the first option is $142.50. The amount earned by the second option is $7 x 20 = $140. So, the first option pays more. 20

9. Homework: P. 469 #2,3,4 (Every other), 6,8 - 11