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# Patterns and sequences

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Presentation on sequences that are Arithmetic, Geometric, and neither.

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### Patterns and sequences

1. 2. <ul><li>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. </li></ul><ul><li>Would the common difference be a positive or a negative number in a sequence that went down? </li></ul><ul><li>For example, what is the common difference in this sequence? </li></ul><ul><ul><ul><ul><ul><li>11, 9, 7, 5, 3, … </li></ul></ul></ul></ul></ul>
2. 3. <ul><li>Try writing a rule for this sequence: </li></ul><ul><ul><ul><ul><ul><li>2, 5, 8, 11, … </li></ul></ul></ul></ul></ul><ul><li>It starts with: ________ </li></ul><ul><li>It goes up by: _________ </li></ul><ul><li>Again, each term of an arithmetic sequence goes up by a fixed amount, which is called the ____________________. </li></ul>
3. 4. <ul><li>Each term of a geometric sequence is found by multiplying the previous term by a fixed number. This ratio is called the common ratio . </li></ul><ul><li>Would the common ratio be a whole number or a fraction in a sequence that went down? </li></ul><ul><li>Identify the common ratio in this sequence… </li></ul><ul><li>27, 9, 3, 1, …….. </li></ul>
4. 5. <ul><li>Sequences are neither arithmetic or geometric when they have no common difference or ratio. </li></ul><ul><li>For example, look at this sequence… </li></ul><ul><li>1, 4, 9, 16, 25, … </li></ul><ul><li>What is the rule for this sequence? Why is it not an arithmetic or geometric sequence? </li></ul>
5. 6. <ul><li>Here is an another example of a sequence that is neither arithmetic or geometric: </li></ul><ul><li>You can use algebraic expressions to describe the terms of many different sequences... </li></ul>
6. 7. <ul><li>4, 12, 20, 28, 36, … </li></ul><ul><li>Is it an arithmetic sequence, geometric sequence, or neither ? </li></ul><ul><li>What is the common difference or common ratio of this sequence? </li></ul><ul><li>The next three terms are: . </li></ul>
7. 8. <ul><li>10, 11, 13, 16, 20, … </li></ul><ul><li>Is it an arithmetic sequence, geometric sequence, or neither ? </li></ul><ul><li>What is the common difference or common ratio of this sequence? </li></ul><ul><li>The next three terms are: . </li></ul>
8. 9. <ul><li>3, -9, 27, -81, 243, … </li></ul><ul><li>Is it an arithmetic sequence, geometric sequence, or neither ? </li></ul><ul><li>What is the common difference or common ratio of this sequence? </li></ul><ul><li>The next three terms are: . </li></ul>
9. 10. <ul><li>4, -1, -6, -11, -16, … </li></ul><ul><li>Is it an arithmetic sequence, geometric sequence, or neither ? </li></ul><ul><li>What is the common difference or common ratio of this sequence? </li></ul><ul><li>The next three terms are: . </li></ul>
10. 11. <ul><li>1, 0, 2, 0, 3, … </li></ul><ul><li>Is it an arithmetic sequence, geometric sequence, or neither ? </li></ul><ul><li>What is the common difference or common ratio of this sequence? </li></ul><ul><li>The next three terms are: . </li></ul>
11. 12. <ul><li>100, 20, 4, 0.8, 0.16, … </li></ul><ul><li>Is it an arithmetic sequence, geometric sequence, or neither ? </li></ul><ul><li>What is the common difference or common ratio of this sequence? </li></ul><ul><li>The next three terms are: . </li></ul>