Math 1 - Weebly
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]
[pic]
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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