The document discusses arithmetic and geometric sequences and their key characteristics. An arithmetic sequence has a common difference, while a geometric sequence has a common ratio. Several example sequences are provided and the reader is asked to identify whether they are arithmetic, geometric, or neither and determine their common differences or ratios.

2. The constant amount between terms in an arithmetic sequence is called the common difference . We add the common difference to get to the next term. Would the common difference be a positive or a negative number in a sequence that went down? For example, what is the common difference in this sequence? 11, 9, 7, 5, 3, …

3. Try writing a rule for this sequence: 2, 5, 8, 11, … It starts with: ________ It goes up by: _________ Again, each term of an arithmetic sequence goes up by a fixed amount, which is called the ____________________.

4. Each term of a geometric sequence is found by multiplying the previous term by a fixed number. This ratio is called the common ratio . Would the common ratio be a whole number or a fraction in a sequence that went down? Identify the common ratio in this sequence… 27, 9, 3, 1, ……..

5. Sequences are neither arithmetic or geometric when they have no common difference or ratio. For example, look at this sequence… 1, 4, 9, 16, 25, … What is the rule for this sequence? Why is it not an arithmetic or geometric sequence?

6. Here is an another example of a sequence that is neither arithmetic or geometric: You can use algebraic expressions to describe the terms of many different sequences...

7. 4, 12, 20, 28, 36, … Is it an arithmetic sequence, geometric sequence, or neither ? What is the common difference or common ratio of this sequence? The next three terms are: .

8. 10, 11, 13, 16, 20, … Is it an arithmetic sequence, geometric sequence, or neither ? What is the common difference or common ratio of this sequence? The next three terms are: .

9. 3, -9, 27, -81, 243, … Is it an arithmetic sequence, geometric sequence, or neither ? What is the common difference or common ratio of this sequence? The next three terms are: .

10. 4, -1, -6, -11, -16, … Is it an arithmetic sequence, geometric sequence, or neither ? What is the common difference or common ratio of this sequence? The next three terms are: .

11. 1, 0, 2, 0, 3, … Is it an arithmetic sequence, geometric sequence, or neither ? What is the common difference or common ratio of this sequence? The next three terms are: .

12. 100, 20, 4, 0.8, 0.16, … Is it an arithmetic sequence, geometric sequence, or neither ? What is the common difference or common ratio of this sequence? The next three terms are: .