Download Warm Up - PBworks

Warm Up
Graph the sequence 128, 64, 32, 16, 8
• Make a table pairing each term with its position number
Position (x)
Term (y)
1
128
2
64
What function does your
scatterplot look like?
In fact, a ______________
sequence is a
_______________ function.
Domain:
Range:
3
32
4
16
5
8
Geometric
Sequences
Unit 6 Notes (Part 1)
AA1.CC
What does geometric mean?
• A geometric sequence is a list of
numbers with a common ratio (r)
–A common ratio means you are
MULTIPLYING the same amount
between each term
Ex.1 Determine if the sequence is
geometric. If so, find the common
ratio.
1) -2, 6, -18, 54, …
2) 2, 4, 6, 8, …
3) -1, -5, -25, -125, …
Geometric Explicit Formula
n 1
n
1
a ar
First Term
Common ratio
Yep, you need
to memorize
this one too!
Ex.2 Given the explicit formula for a geometric
sequence, find the common ratio and the 2nd
and 6th term.
n 1
n
a  3(2)
First Term
2nd term:
-6
6th term:
-96
Common ratio
Ex.3 Given the explicit formula for a geometric
sequence, find the common ratio and the first five
n 1
terms.
a n  5
Term # Work Work
11
(

1
)(
5
)
1
1
2 1
(

1
)(
5
)
2
2
31
(

1
)(
5
)
3
3
4 1
(

1
)(
5
)
4
4
(1)(5)51
5
5
Term
Term
-1
-1
-5
-25
-125
-625
Geometric Recursive Formula
Previous Term
Common ratio
𝑎𝑛 = 𝑎𝑛−1 × 𝑟
𝑎1 = 𝑓𝑖𝑟𝑠𝑡 𝑡𝑒𝑟𝑚
Ex.4 Given the recursive formula for a
geometric sequence, find the common ratio
and the first five terms.
an  an 1  2
a1  3
Term
Term# #
Work
Work
Term
Term
11
“given”
“given”
33
22
3  2
-6
33
 6  2
12
4
12  2
-24
5
 24  2
48
4
5
Common
ratio
Practice
Find r and first 5 terms
Explicit
a n  2 ( 4 )
n 1
Common
ratio
2, -8, 32, -128, 512
Recursive
an  an 1  4
a1  3
Common
ratio
3, 12, 48, 192, 768
Ex.5 Find the common ratio, recursive formula,
and the Explicit Formula
Just like arithmetic recursive, you are relying on the
previous answer. Find the pattern again (this will be
your “r”)
-2, 6, -18, 54, …
Ratio
Recursive
-3
𝒂𝒏 = 𝒂𝒏−𝟏 × −𝟑
𝒂𝟏 = −𝟐
Explicit
𝒂𝒏 = −𝟐(−𝟑)𝒏−𝟏
Practice
Find the common ratio, recursive formula, and the explicit formula.
1) 1, 2, 4, 8, …..
Ratio
2
Recursive
𝑎𝑛 = 𝑎𝑛−1 × 2
𝑎1 = 1
2) -3, 12, -48, 192, …
Ratio
-4
Recursive
𝑎𝑛 = 𝑎𝑛−1 × −4
𝑎1 = −3
Explicit
𝑎𝑛 = 2𝑛−1
Explicit
𝑎𝑛 = −3(−4)𝑛−1
Homework:
(Part 1)
Geometric sequence
worksheet
#1-14