day 7 - geometric...
Post on 28-Sep-2020
1 Views
Preview:
TRANSCRIPT
Day 7 Geometric Sequences.notebook
1
March 28, 2018
Feb 264:35 PM
Warm-Up 3/28/18
1. The population of stray cats at the gas station doubles every 4 months. After 12 months, how many cats are roaming around if there were initially 9 cats?
2. Find the value of $500 deposited for 20 years in an account paying 15% annual interest compounded quarterly.
Day 7 Geometric Sequences.notebook
2
March 28, 2018
Mar 56:58 AM
Learning Objectives3/27/18
I can write explicit and recursive formulas for geometric sequences.
Day 7 Geometric Sequences.notebook
3
March 28, 2018
Mar 2111:05 AM
Opening:
• What is a sequence• Sequences can be
finite or infinite. • Can you give me
examples of sequences?
Day 7 Geometric Sequences.notebook
4
March 28, 2018
Mar 258:53 AM
Day 7 Geometric Sequences.notebook
5
March 28, 2018
Mar 258:54 AM
,or common ratio.
Day 7 Geometric Sequences.notebook
6
March 28, 2018
Mar 259:03 AM
Two ways to define sequences:1. Closed/Explicit:• Can directly find nth term • NOT required to list 1st term• Uses formula an = a1(r)n-1
for geometric sequences
2. Recursive:• Relates each term in the sequence to a
previous term• Must ALWAYS state 1st term• Requires formula that relates the nth
term to the (n-1)th term
Day 7 Geometric Sequences.notebook
7
March 28, 2018
Mar 258:55 AM
Day 7 Geometric Sequences.notebook
8
March 28, 2018
Mar 258:56 AM
Day 7 Geometric Sequences.notebook
9
March 28, 2018
Mar 258:56 AM
Day 7 Geometric Sequences.notebook
10
March 28, 2018
Mar 258:57 AM
Day 7 Geometric Sequences.notebook
11
March 28, 2018
Mar 259:05 AM
Examples - Finding the Nth Term
Day 7 Geometric Sequences.notebook
12
March 28, 2018
Mar 259:06 AM
Finding Terms Using an Explicit Rule
Day 7 Geometric Sequences.notebook
13
March 28, 2018
Mar 259:08 AM
Day 7 Geometric Sequences.notebook
14
March 28, 2018
Mar 259:09 AM
Examples - Finding Terms Using a Recursive Rule
Day 7 Geometric Sequences.notebook
15
March 28, 2018
Mar 259:11 AM
Creating a Recursive Rule
Day 7 Geometric Sequences.notebook
16
March 28, 2018
Mar 259:12 AM
Day 7 Geometric Sequences.notebook
17
March 28, 2018
Mar 259:14 AM
Day 7 Geometric Sequences.notebook
18
March 28, 2018
Mar 259:14 AM
Day 7 Geometric Sequences.notebook
19
March 28, 2018
Mar 259:15 AM
Day 7 Geometric Sequences.notebook
20
March 28, 2018
Mar 259:15 AM
Day 7 Geometric Sequences.notebook
21
March 28, 2018
Mar 259:16 AM
Day 7 Geometric Sequences.notebook
22
March 28, 2018
Mar 259:16 AM
Class Work 3/27/18
Day 7 Geometric Sequences.notebook
23
March 28, 2018
Mar 259:17 AM
Day 7 Geometric Sequences.notebook
24
March 28, 2018
Mar 259:18 AM
Day 7 Geometric Sequences.notebook
25
March 28, 2018
Mar 259:18 AM
Day 7 Geometric Sequences.notebook
26
March 28, 2018
Mar 259:22 AM
Closing 3/28/18
Geometric or Arithmetic?
Common ratio? Common difference?
Day 7 Geometric Sequences.notebook
27
March 28, 2018
Mar 215:21 PM
-1, 6, -36, 216,... 35, 32, 29,26, ...
-3, -23, -43, -63, ....
-3, -15, -75, -375, ..
4, 16, 36, 64, ...
-34, -64, -94, -124,.
-7, -9, -11, -13,...
-1, 1, 4, 8, ...
1, -5, 25, -125, ...
9, 14, 19, 24, ...
21, 15, 9, ...
-4, 1, 6, 11, ...
7, -7, 7, -7, ...
1/2, 3/2, 5/2, ...
2, -3, -8, ...
1, 3, 9, 27, ...
2, 10, 50, ...
-17, -13, -9, ...
8, 3, -2, ...
12, -6, 3, 3/2, ...
Day 7 Geometric Sequences.notebook
28
March 28, 2018
Mar 259:22 AM
Day 7 Geometric Sequences.notebook
29
March 28, 2018
Mar 216:11 PM
Closing: Class Discussion
» What name can also be given to the type of pattern produced in a geometric sequence?
» Do geometric sequences form an exponential pattern?
» When r is a proper fraction, do we have exponential decay or growth?
» Give me an example of a geometric sequence that represents exponential decay?
top related