1. Example: Finding the nth Term
M3U1D4 Warm Up
Find the 9th term of the geometric sequence
7, 21, 63, . . .
a1 = 7
an = a1rn – 1 = 7(3)n – 1
a9 = 7(3)9 – 1 = 7(3)8
= 7(6561) = 45,927
The 9th term is 45,927.
NEW SEATS!!!!
Example: Finding the nth Term

2. Homework Check:
1150
283

3. Homework Check:

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

5. M3U1D4
Geometric Series
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. First Let’s Look at a Geometric Finite Series

7. WRITE THESE FORMULAS DOWN ON YOUR HINTS CARD!!!
Vocabulary of Geometric Sequences and Series (Universal)
FINITE!!!
WRITE THESE FORMULAS DOWN ON YOUR HINTS CARD!!!

8. Example 1: Let’s Review Geometric Sequences and add!!!
And S9
1/2 x 9
NA, yet…
2/3
Sn = )

9. Example 2:
1/2 7 x
127/128

10. Now Let’s Look at a Geometric Infinite Series

11. Let’s summarize what we know and add to it!
1, 4, 7, 10, 13, ….
Infinite Arithmetic
No Sum
3, 7, 11, …, 51
Finite Arithmetic
1, 2, 4, …, 64
Finite Geometric
1, 2, 4, 8, …
Infinite Geometric
r > 1
r < -1
No Sum
Infinite Geometric
-1 < r < 1

12. Example 3:
Find the sum, if possible:

13. Example 4:
Find the sum, if possible:

14. Example 5:
Find the sum, if possible:

15. YOU TRY!
Find the sum, if possible:

16. YOU TRY!
Find the sum, if possible:

17. Example 6: Find n for the series in which 5 y x 440 3
Graph on positive window
X = 16

18. Example 7: A Real World Example!
An auditorium has 20 rows of seats. There are 20 seats in the first row, 21 seats in the second row, 22 seats in the third row, and so on. How many seats are there in all 20 rows?
(n-1)

19. Example 8:
The Bouncing Ball Problem – Version A
A ball is dropped from a height of 50 feet. It rebounds 4/5 of
it’s height, and continues this pattern until it stops. How far
does the ball travel? 50 40 40 32 32
25.6
25.6
Notice…Drawing a Picture made visualizing and solving EASIER!!!

20. YOU TRY!
The Bouncing Ball Problem – Version B
A ball is thrown 100 feet into the air. It rebounds 3/4 of
it’s height, and continues this pattern until it stops. How far
does the ball travel?
100
100 75 75
225/4
225/4
REMEMBER…Drawing a Picture made visualizing & solving easier!!!

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

22. 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

23. Project
UPDATE THE PERCENTAGES AS FOLLOWS: Don’t forget…. DUE Sept. 15th !!! See me personally if you’ve already started calculations

24. Classwork:
U1D4 Back Side WS odds
#1 reads:

25. Homework:
Finish CW