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Grade 11 Functions (MCR3U)

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1 Grade 11 Functions (MCR3U)
Unit 5: Pascal’s Triangle, Binomial Theorem, Sequences & Series Arithmetic Series Mr. Choi © 2018 E. Choi – MCR3U - All Rights Reserved

2 What is a Series? S5  the sum of the first 5 terms
A series is the sum of terms of a sequence. The sum of the first n terms in a sequence is denoted as Sn. S5  the sum of the first 5 terms Arithmetic Series © 2018 E. Choi – MCR3U - All Rights Reserved

3 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 …, is called an arithmetic series. Arithmetic Series © 2018 E. Choi – MCR3U - All Rights Reserved

4 Arithmetic Series Formula
Recall: Arithmetic Sequence formula The Sum of the First n terms of an Arithmetic Series Rewrite this series in reverse order Add this two rows together There are n terms in total a +(n - 1)d Formula 2 or Formula 1 Arithmetic Series © 2018 E. Choi – MCR3U - All Rights Reserved

5 Example 1 – Sum of a Series given the first term
Find the sum of the first 60 terms of each series. Arithmetic Series © 2018 E. Choi – MCR3U - All Rights Reserved

6 Example 2 – Sum of a series given first and last terms
Find the sum of the arithmetic series 50 50 50 There are 50 terms in the series. Arithmetic Series © 2018 E. Choi – MCR3U - All Rights Reserved

7 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 20 20 The amount earned by the first option is $ The amount earned by the second option is $7 x 20 = $140. So, the first option pays more. Arithmetic Series © 2018 E. Choi – MCR3U - All Rights Reserved

8 Homework: Text Book: P. 400 #1-8 (acd for all), 11,12,14 Work Sheet:
Check the website for updates Arithmetic Series © 2018 E. Choi – MCR3U - All Rights Reserved

9 End of Lesson Arithmetic Series
© 2018 E. Choi – MCR3U - All Rights Reserved

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