1. M3U1D5 Warm Up
One morning (day 1), three people start a chain letter via . Each of them sends a message to five other people with the instructions that the receiver must forward the message to 5 other people the following morning. Assume this process continues each morning without any repetition of recipients.
Calculate the number of new recipients to the message on
day 2, day 3, day 4 and day 5.
2. Identify the pattern in the sequence of numbers generated in the first activity – i.e. come up with the ‘common ratio’
3. Develop a formula for the nth term of the sequence and use it to calculate the number of new recipients on the 7th day
r = 5
an = 15(5)n-1
234,375

2. Homework Check:

3. Homework Check:

4. Collect Parent Letters
Homework Check:
Document Camera
Collect Parent Letters

5. Series and Sequences Review
M3U1D5
Series and Sequences Review
Objective:
To write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. F-BF.2

6. Finally, how can we evaluate these in the calculator???

7. Graphing Utility: Terms and Sum of a Sequence
Graphing Utility: Find the first 5 terms of the geometric sequence an = 2(1.3)n.
end value
variable
beginning value
List Menu:
Graphing Utility: Find the finite sum
upper limit
List Menu:
variable
lower limit
Graphing Utility: Terms and Sum of a Sequence

8. Hints Card Make sure your card matches mine
Hints Card Make sure your card matches mine. Nothing else may be on the card if you intend to use it on the Quest! (Document Camera)

9. Convergent and Divergent Series clarified

10. Convergent and Divergent Series
If the infinite series has a sum, or limit, the series is convergent.
If the series is not convergent, it is divergent.

11. Ways To Determine Convergence/Divergence
1. Arithmetic – since no sum exists, it diverges
2. Geometric:
If |r| > 1, diverges
If |r| < 1, converges since the sum exists (i.e. -1 < r < 1)

12. Example
Determine whether each arithmetic or geometric series is convergent or divergent.
1/8 + 3/20 + 9/ /
r=6/5  r >1  divergent
Arithmetic series  divergent
/5 + 13/
r=1/5  -1 < r < 1  convergent

13. Review for Quiz!

14. OBJECTIVES:
Quiz Review:
Distinguish between arithmetic and geometric sequences
Evaluate arithmetic and geometric sequences
Write sequences in recursive and explicit format
Solve real - world situations involving sequences
Distinguish between arithmetic and geometric series
Evaluate arithmetic and geometric series
Compound Interest

15. Don’t forget…. DUE Sept. 15th !!!
Project
Don’t forget…. DUE Sept. 15th !!!

16. Quiz Review Handout odds WE WILL CHECK THIS PERIOD!!!
Classwork:
Quiz Review Handout odds
WE WILL CHECK THIS PERIOD!!!

17. Homework:
Study for QUIZ