1. Knight’s Charge 8/26/15 Review Have your homework out on your desk (including your triangle).

2. Textbooks  Write your name in your textbook in the appropriate place on the inside front cover.  Fill out your index card as follows:  Turn in your index card.  Remember: These books cost around $108, so TAKE CARE OF THEM. You need to COVER YOUR BOOK!! Student Name Glencoe Precalculus Book Book #:___________ Book Condition: NEW

3. Check Homework 8/26/15 Set D Practice Wkst

4. Sequences and Series Unit 1

6. Consider this: Intro to Sequences  A pyramid of logs has 2 logs in the top row, 4 logs in the second row from the top, 6 logs in the third row from the top, and so on, until there are 200 logs in the bottom row.

7. A pyramid of logs has 2 logs in the top row, 4 logs in the second row from the top, 6 logs in the third row from the top, and so on, until there are 200 logs in the bottom row. Intro to Sequences  Write and interpret the first 10 terms of the sequence of numbers generated from the example.  Identify the pattern in the sequence of numbers.  Write the formula for the nth term of the sequence and use it to find the number of logs in, say, the 76th row  Compute the number of logs in the first 12 rows combined.  What is the total number of logs in the pyramid?

8. Intro to Arithmetic Series: One of the most famous legends in the lore of mathematics concerns German mathematician Carl Friedrich Gauss.  One version of the story has it that in primary school after the young Gauss misbehaved, his teacher, J.G. Büttner, gave him a task: add the numbers from 1 to100. The young Gauss reputedly produced the correct answer within seconds, to the astonishment of his teacher and his assistant, Martin Bartels. Can you?  Gauss's realized that pairwise addition of terms from opposite ends of the list yielded identical intermediate sums: 1 + 100 = 101, 2 + 99 = 101, 3 + 98 = 101, and so on, for a total sum of 50 × 101 = 5050. Arithmetic Series

9. General Sequences

10. Fill in the chart. General Sequences SEQUENCE IMPLICIT FORMULA EXPLICIT FORMULA

11. Find the first six terms for each sequence:

12. Arithmetic, Geometric, or Neither? GEOMETRIC ARITHMETIC NEITHER Fibonacci Sequence

13. Formal Definition of an Arithmetic Sequence Arithmetic Sequences

14. Example: Write an explicit formula for the sequence {10, 15, 20, 25, …}. Arithmetic Sequences  Note: this sequence is arithmetic with a common difference (d) of 5.  Make a table of values for the terms of the sequence. Then graph the table. What do you notice about the graph? It’s LINEAR…… Can you write the equation of the line/sequence now?

15. Example: Write an explicit formula for the sequence {10, 15, 20, 25, …}. Arithmetic Sequences

16. Example: Fill in the chart for each arithmetic sequence shown. Arithmetic Sequences SEQUENCE IMPLICIT FORMULA EXPLICIT FORMULA 100 th term

17. Arithmetic Sequences

19. Arithmetic Means  Example: Form an arithmetic sequence that has 3 arithmetic means between 15 and 35.  Example: Form an arithmetic sequence that has 4 arithmetic means between 13 and 15.

20. Arithmetic SERIES

21. Sum of a FINITE Arithmetic Sequence Arithmetic Series

22. Example: Given the sum of the first 20 terms of a sequence that starts with 5 is 220, find the 20 th term. Arithmetic Series

23.  the common difference.  the 15 th term.  the explicit formula for the sequence.  the sum of the first 20 terms of the sequence. Arithmetic Series

24. Application of Arithmetic Series A corner section of a stadium has 14 seats along the front row and adds one more seat to each successive row. If the top row has 35 seats, how many seats are in that section? Arithmetic Series

25. Homework Arithmetic Sequences  Pre-precal review Set J Extra Practice  Textbook p. 605 #1-25 Odd  Sign up to receive texts from me (assignments, extra credit, etc.)  2 nd period: Text the message honeycutt2 to 81010  3 rd period: Text the message honeycutt3 to 81010