1. Arithmetic Sequences

2. Lightning Strike
During a thunderstorm, you can estimate your distance from a lightning strike by counting the number of seconds from the time you see the lightning until the time you hear thunder.
A table of the time (in seconds) and the distance (in miles) creates a sequence.

3. Vocabulary
When we list the times and distances in order, each list forms a sequence.
Sequence--A list of numbers that may form a pattern.
Term--Each number in a sequence.

4. How to Identify Arithmetic Sequences
Khan Academy--Intro to Arithmetic Sequences

5. Arithmetic Sequences
Arithmetic Sequence---a sequence of numbers such that the difference between the consecutive numbers is constant.
Common Difference--the difference between 2 numbers in a sequence.
***The Common Difference is the “d” part of the formula for the sequence.
We can define a sequence explicitly or recursively.
*** The “n” part of the formula represents the number of term for which you are evaluating the sequence.

6. What’s the next term in the sequence?

7. Find any term of an arithmetic sequence.

8. Explicit Formula for Arithmetic Sequences
Definition--a formula that allows direct computation of any term of a sequence.
**This way is easiest when computing a specific term!**
Looks Like:

10. Recursive Formula for Arithmetic Sequences
Definition--a formula that requires computation of all previous terms in order to find the value of an
Looks Like:

12. Questions
How is identifying an arithmetic sequence similar to identifying a function rule?
How do I write an arithmetic sequence explicitly?
What is a recursive formula?
How do I write an arithmetic sequence recursively?
How do you know what number to substitute for d?
How do you know what number to substitute for n?
What is a real world situation that can be modeled with an arithmetic sequence?

13. Journal
Explain how to determine if a sequence is arithmetic or not.

14. Homework P. 209 #9-12 (Follow book directions).
P. 209 #28-31 (Write a formula for the sequence explicitly and recursively. Then find the given term of each sequence.)