Download 5-8 Geometric Sequences.notebook

5­8 Geometric Sequences.notebook
April 24, 2014
LT: •• I can identify a geometric sequence.
I can write and use a function for a geometric sequence.
p.5
What is a
a sequence in which each term after the first is found by geometric _____________ the previous term by a non­zero constant.
sequence?
Steps for
identifying
sequences as geometric:
1. Look for a constant ___________ between terms. (Like yesterday)
2. If no constant difference, look for a constant _________(divide) between terms. This is your 'b' (growth).
3. Identify your starting value. This is your ___.
4. Substitute __ and __ into the equation f(x) = a(b)x
x
y
4, 8, 16, 32, 64, ...
term #
Rule for Sequence (b): ______
Starting Amount (a): ______
Equation: ______________
7th term: ______
(so x = ___ for the 7th term)
400, 200, 100, 50, ...
Rule for Sequence (b): ______
Starting Amount (a): ______
Equation: ______________
7th term: ______
(so x = ___ for the 7th term)
1x, 5x2, 25x3, 125x4 Rule for Sequence (b): ______
Starting Amount (a): ______
Equation: ______________
Summary:
7th term: ______
(so x = ___ for the 7th term)
5­8 Geometric Sequences.notebook
CW p. 6­7 (1,4,5,7) April 24, 2014
P p. 6­8 (all) 1) 4, 12, 36, 108, …
Rule for Sequence (b): ______ 7th term: ___
Starting Amount (a): ____ (so x = __ for the 7th term)
Equation: _________
2) 0.25, 0.5, 1, 2, …
Rule for Sequence (b): ______ 7th term: ___
Starting Amount (a): ____ (so x = __ for the 7th term)
Equation: _________
3) 4, 2, 1, 0.5, …
Rule for Sequence (b): ______ 7th term: ___
Starting Amount (a): ____ (so x = __ for the 7th term)
Equation: _________
4) 8, 2, 0.5, 0.125, …
Rule for Sequence (b): ______ 7th term: ___
Starting Amount (a): ____ (so x = __ for the 7th term)
Equation: _________
5)
Rule for Sequence (b): ______ 7th term: ___
Starting Amount (a): ____ (so x = __ for the 7th term)
Equation: _________
6) 2, 2, 2, 2, …
Rule for Sequence (b): ______ 7th term: ___
Starting Amount (a): ____ (so x = __ for the 7th term)
Equation: _________
p.6
5­8 Geometric Sequences.notebook
April 24, 2014
7) 1 , 1 , 1 , ...
27
9
3
Rule for Sequence (b): ______ 7th term: ___
Starting Amount (a): ____ (so x = __ for the 7th term)
Equation: _________
8) 1, 2, 4 ,8...
Rule for Sequence (b): ______ 7th term: ___
Starting Amount (a): ____ (so x = __ for the 7th term)
Equation: _________
9) 5, 5x2, 5x4, 5x6.....
Rule for Sequence (b): ______ 7th term: ___
Starting Amount (a): ____ (so x = __ for the 7th term)
Equation: _________
10) 7, 35, 175, 875....
Rule for Sequence (b): ______ 7th term: ___
Starting Amount (a): ____ (so x = __ for the 7th term)
Equation: _________
11) a2, 2a2, 4a2, 8a2....
Rule for Sequence (b): ______ 7th term: ___
Starting Amount (a): ____ (so x = __ for the 7th term)
Equation: _________
12) 320, 80, 20, 5...
Rule for Sequence (b): ______ 7th term: ___
Starting Amount (a): ____ (so x = __ for the 7th term)
Equation: _________
p.7
5­8 Geometric Sequences.notebook
April 24, 2014
p.8
'Remembering'
13. Find the base of the right triangle below.
14. The base of a ladder is placed 6 feet from a wall. The top of the ladder rests 8 feet up on the wall. How long is the ladder?
x
15.
{
Solve the system of equations y = 6 ­ 2x
y = 3(2x + 4)
16.
What is the slope between the two points (8, 3) and (8, ­1)?
5­8 Geometric Sequences.notebook
IF
Box 3
Write the first 4 terms of any arithmetic sequence that has a rule of +7. Grab a ew IF
April 24, 2014
Checking: p.2­4
Write an equation for your sequence.
What is the 31st term of your sequence?
5­8 Geometric Sequences.notebook
p.2­4 answers
April 24, 2014
5­8 Geometric Sequences.notebook
April 24, 2014
5­8 Geometric Sequences.notebook
April 24, 2014
5­8 Geometric Sequences.notebook
April 24, 2014
1­4
2­4
5­8
6­8
5­8 Geometric Sequences.notebook
April 24, 2014
5­8 Geometric Sequences.notebook
April 24, 2014
LT: •• I can identify a geometric sequence.
I can write and use a function for a geometric sequence.
p.5
What is a
a sequence in which each term after the first is found by geometric multiplying
_____________ the previous term by a non­zero constant.
sequence?
Steps for
identifying
sequences as geometric:
1. Look for a constant ___________ between terms. (Like yesterday)
difference
2. If no constant difference, look for a constant _________(divide) between terms. This is your 'b' (growth).
quotient
a
3. Identify your starting value. This is your ___.
x
b
a
4. Substitute __ and __ into the equation f(x) = a(b)
x
y
4, 8, 16, 32, 64, ...
term #
Rule for Sequence (b): ______ 7th term: ___
Starting Amount (a): ____ (so x = __ for the 7th term)
Equation: _________
400, 200, 100, 50, ...
Rule for Sequence (b): ______ 7th term: ___
Starting Amount (a): ____ (so x = __ for the 7th term)
Equation: _________
1x, 5x2, 25x3, 125x4 Rule for Sequence (b): ______ 7th term: ___
Starting Amount (a): ____ (so x = __ for the 7th term)
Equation: _________
5­8 Geometric Sequences.notebook
April 24, 2014
All graphs of arithmetic
sequences are LINEAR.
What do the graphs
of an geometric
sequences look like?
gc
5­8 Geometric Sequences.notebook
April 24, 2014
Summary:
Find the common quotient (growth rate "b") by dividing.
5­8 Geometric Sequences.notebook
April 24, 2014
Geometric Sequences
CW p. 6­7 (1,4,5,7) P p. 6­8 (all) answers 5­8 Geometric Sequences.notebook
April 24, 2014
p.6­8 answers
1/512 or 0.00195
5­8 Geometric Sequences.notebook
April 24, 2014
5­8 Geometric Sequences.notebook
April 24, 2014