1. Geometric sequences

2. Have a common difference MULTIPLY to get next term
Arithmetic Sequences
Geometric Sequences
ADD To get next term
Have a common difference
MULTIPLY to get next term
Have a common ratio

3. Try to think of some geometric sequences on your own!
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!

4. Find r for the following sequences
4, 8, 16, 32...
r=2
r=3
8, 24, 72,
r=4
6, 24, 96,
No common ratio!
Geometric
Sequence
5, 10, 15, 20...

5. Writing a rule
To write a rule for the nth term of a geometric sequence, use the formula:

6. Writing a rule
Write a rule for the nth term of the sequence 6, 24, 96, 384,
Then find
This is the general rule. It’s a formula to use to find any term of this sequence.
To find , plug 7 in for n.

7. Writing a rule
Write a rule for the nth term of the sequence 1, 6, 36, 216, 1296,
Then find
This is the general rule. It’s a formula to use to find any term of this sequence.
To find , plug 8 in for n.

8. Writing a rule Write a rule for the nth term of the sequence
7, 14, 28, 56, 128,
Then find

9. (when you're not given the first term)
Writing a rule
(when you're not given the first term)
One term of a geometric sequence is The common ratio is r = Write a rule for the nth term.

10. (when you're given two non-consecutive terms)
Writing a rule
(when you're given two non-consecutive terms)
One term of a geometric sequence is and one term is
Step 1: Find r
-divide BIG
small
-find the distance between the two terms and take that root.
Step 2: Find Plug r, n, and into your equation. Then, solve for
Step 3: Write the equation using r and

11. (when you're given two non-consecutive terms)
Writing a rule
(when you're given two non-consecutive terms)
Write the rule when and

12. Graphing the sequence 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