1. Arithmetic and Geometric Sequences
Chapter 10.1

2. Sequence - a set of numbers in a particular order or pattern
Infinite Sequences - continues with out end
Finite Sequences - contains a limited number of terms
Arithmetic Sequence
An arithmetic sequence is a sequence of numbers in which each term is found by adding a constant by the previous term. This constant value is call a common difference.
Example: Find the next four terms of the arithmetic sequence 7, 11, 15, … .

3. Find the common difference and the next four terms of each arithmetic sequence.
1. 106, 111, 116, …
2. –28, –31, –34, …
3. 207, 194, 181, ...
4. –30, –20, –10, …
5. 13, 7, 1, …
6. 151, 177, 203, …

4. SEATING Kay is trying to find her seat in a theater.
The seats are numbered sequentially going left
to right. Each row has 30 seats.
The figure shows some of the chairs in the left corner near the stage. Kay is at seat 129, but she needs to find seat 219. She notices that the seat numbers in a fixed column form an arithmetic sequence. What are the numbers of the next 4 seats in the same column as seat 129 going away from the stage? Where does Kay have to go to find her seat? In what row and column is her seat?

5. Sequence - a set of numbers in a particular order or pattern
Infinite Sequences - continues with out end
Finite Sequences - contains a limited number of terms
Geometric Sequence
An geometric sequence is a sequence of numbers in which each term is found by multiplying a nonzero constant by the previous term. This constant value is call a common ratio.
Example: Find the next three terms of the geometric sequence 2, 6, 18 … .

6. Find the common difference and the next four terms of each arithmetic sequence. Then graph the sequence.
, 1 4 , 1, …
2. 20, 4, 4 5 , …
3. –24, –12, –6, …
25 , 2, 10, …
4. 6⅓, 19, 57, …
5. 13, 26, 52, …
6. 2/5, 2, 10 …

7. BACTERIA Streptococcus pneumoniae is one of the bacteria that can cause pneumonia. This bacteria can double its population in 20 minutes. If a sample started with 300 bacteria and doubled every 20 minutes, use the geometric series formula to calculate the number of bacteria in the sample after 80 minutes