Download 11.13.14 geometric

Arithmetic Sequences
1, 4, 7, 10, 13...
8,15,22,29...
•ADD To get next term
•Have a common difference
Geometric Sequences
2, 4, 8, 16, 32..
1
9,  3, 1,  ..
3
•MULTIPLY to get next term
•Have a common ratio
In a geometric sequence, the ratio of any term to the
previous term is constant.
You keep multiplying by the SAME number
each time to get the sequence.
This same number is called the common ratio
and is denoted by r
8
16
32
 2,  2,  2
4
8
16
24
72
216
 3,
 3,
3
8
24
72
24
96
384
 4,
 4,
4
6
24
96
No common ratio!
10
15
 2,  1.5
5
10
Geometric
Sequence
To write a rule for the nth term of a geometric sequence,
use the formula:
nth term of geometric sequence an  a1r n1
r  common ratio
a1  First term
an  nth term
n  number of terms
Example 1: Write a rule for the nth term of the sequence
6, 24, 96, 384, . . .Then find a7
an  a1r
n1
a1  6
n 1
an  6(4)
24
r  6 4
To find a , plug 7 in for n.
7
n7
an  6(4) n 1
7 1
a7 
a7  6(4)
a7  6(4)
6
This is the general
rule. It’s a
formula to use to
find any term of
this sequence.
a7  6(4096)  24,576
Example 2: Write a rule for the nth term of the sequence
1, 6, 36, 216, 1296, . . .Then find a
8
a1  1
6
r  1 6
n 8
an 
an  a1r
n1
an  1(6)
This is the general
rule. It’s a
formula to use to
find any term of
this sequence.
n 1
To find
a8 , plug 8 in for n.
n 1
an  1(6)
8 1
a8  1(6)
7
a8  1(6)
a8  6  279,936
7
Now You Try: Write a rule for the nth term of the sequence
7, 14, 28, 56, 128, . . .
Then find a6
Example 3: One term of a geometric sequence is a3  18 .
The common ratio is r = 3.
Write a rule for the nth term.
a1 
r 3
n3
an  a3  18
n is the number of the known term
an is the value of the known term
Let’s graph the sequence from Example 3.
Create a table of values.
Why do we pick all positive whole
numbers?
Domain, Input, x
Range, Output, y
What kind of function is this?
What is a?
What is b?