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Coordinate Algebra: Unit 3

Name___________________  Date_________________ Period________

Lesson 6: Arithmetic Sequences Notes

|Standard and Skills |

|F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* |

| |

|SWBAT write arithmetic sequences explicitly |

|SWBAT write arithmetic sequences recursively |

Everyday a radio station asks a question for a prize of $150. If the fifth caller does not answer correctly, the prize money increased by $150 each day until someone correctly answers their question. Make a list of the prize money for a week from Monday to Friday if no one gets it right.

Given this information, fill out the table accordingly:

|a1 |$150 |

|a2 | |

|a3 | |

|a4 | |

|a5 | |

|an | |

Important Definitions

← Sequence: A function whose domain is a set of ________________________________. It can be specified by an ________________ or ____________________.

← An Arithmetic Sequence is a sequence that has a _______________ common difference.

← The values in the range of the sequence are called the _______________________________________.

Example 1: Given the rule an = 6n – 4 , find the next term in the sequence.

2, 8, 14, 20, ___ , ___,……. _____ .

Quick Check! Write the first five terms of the sequence. Identify the domain and range.

1. [pic]

2. [pic]

Arithmetic Sequence Rule

Explicit Formula

Recursive Formula an= an-1 + d

an = the nth term d = the common difference

a1 = the first term of the sequence n = the number of the term in the sequence

Example 2: Write the rule for the nth term of the sequence 2, 6, 10, 14

Identify the first term

Identify the common difference between each of the values.

Write the rule _________________________

Quick Check! Write a rule for the nth term.

3. 3, 5, 7, 9, ______

4. 2, 6, 10, 14, ______

5. 7, 4, 1, -2, ______

Example 3: Find a specific term in a sequence.

Find the 21st term in the sequence by writing a rule.

1, 10, 19, 28

Quick Check! Find the 7th term in the sequence.

1. [pic]

2. [pic]

3. [pic]

Independent Practice

Find the first five terms of the sequence.

4. [pic]

5. [pic]

6. [pic]

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7. What is the seventh term of the sequence [pic]

a. [pic]

b. 5

c. 10

d. 14

8. [pic]

For each sequence, describe the pattern, write the next term, and write a rule for the nth term.

9. [pic]

10. [pic]

EOCT Practice Problems

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