1. Note: Remove 97-103o from tonight’s hw
11.1- Sequences and Series
Note: Remove o from tonight’s hw

2. Factorial Expressions
Simplify each expression.

3. Introduction
What is a sequence? A sequence is an ordered list of numbers that follows a pattern.
The domain of a sequence is the set of all whole numbers and it is implied.
The range of a sequence is all of the numbers listed in the sequence, and can be summarized by its nth term formula (aka general term).
An infinite sequence (eg 1, 4, 7, 10, 13,…) goes on forever.
A finite sequence (eg 2, 7, 12, 17, 22) has an ending.

4. List the 1st 5 terms of the sequence
Assume n begins with 1.

5. Find the terms
List the 1st 5 terms
Find a11.

6. Recursive Sequences
Find the 1st 3 terms of each sequence.

7. Sigma Notation EXAMPLE
∑ is a Greek letter that is used in math to mean “take the sum.” For sequences, the number below ∑ indicates what term to begin the sum with; while the number below ∑ indicates the final term number to include in the sum. The notation to the right indicates what pattern to follow to obtain the terms.
EXAMPLE
This notation tells us to add the 1st (i=1) through the 5th term of the sequence following the pattern “3i+2.”

8. Sigma Notation continued

9. 11.2 – Arithmetic Sequences
Day One Objective: To recognize and write arithmetic sequences

10. Arithmetic Sequence defined
A sequence is considered to be arithmetic if the difference between any two consecutive terms is constant. This difference, d, is called the common difference.
Is the Sequence arithmetic? If so, find d.
Ex1. 2, -3, -8, -13,…
Ex2. 3, 4.5, 5.5, 7, 8, 9.5,…
Ex3. ¼, 5/8, 1, 11/8, 7/4, …

11. Finding the nth term
The formula for the nth term of an arithmetic sequence is:
You must know _______ and _______ in order to find the nth term.
If you know two terms of the sequence (am &an) but not d, you will calculate d using:

12. Find the nth term
Example 1
Example 2

13. Find the nth term
Example 3
Example 4

14. Find the indicated term
Example 5 – Find the 30th term
Example 6 – Find the 15th term