Download geometric-sequences-1

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
What is the difference between an arithmetic sequence
and a geometric sequence?
Try to think of some geometric sequences on your own!
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
Write a rule for the nth term of the sequence
6, 24, 96, 384, . . ..
Then find a
7
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
an 
an  6(4)
an  6(4)
6
This is the general
rule. It’s a
formula to use to
find any term of
this sequence.
an  6(4096)  24,576
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
an  1(6)
7
an  1(6)
an  6  279,936
7
Write a rule for the nth term of the sequence
7, 14, 28, 56, 128, . . ..
Then find a6
One term of a geometric sequence is
r = 3. Write a rule for the nth term.
a1 
r 3
n3
an 18
a3  18
The common ratio is
One term of a geometric sequence is
a3  20 and one term is a6  160
Step 1: Find r
-divide BIG
160
8
20
small
-find the distance between the two terms
and take that root.
63  3
3
Step 2: Find a1 . Plug r, n, and an into your
equation. Then, solve for a1 .
Step 3: Write the equation using r and
a1 .
an  5(2) n 1
82
r2
an  a1r n 1
20  a1 231
20  a1 2 2
20  a1 4 5  a1
Write the rule when
a2  12
and
a4  192 .
an  3(4) n 1
Let’s graph the sequence we just did.
Create a table of values. What kind of
function is this?
What is a? What is b?
Why do we pick all positive whole
numbers?
Domain, Input, X
Range, Output, Y
Does it make sense to connect the dots on our
last graph? Why or why not?