1. 8.1 Defining and Using Sequences and Series

2. Sequences A sequence is an ordered list of numbers.
A finite sequence is a function that has a limited number of terms and whose domain is the finite set {1,2,3,….,n}.
The values in the range are called the terms of the sequence.
Domain: n
Range:

3. Infinite Sequences
An infinite sequence is a sequence that continues without stopping and whose domain is the set of all positive integers.
Finite Sequence: 2, 4, 6, 8
Infinite Sequence: 2, 4, 6, 8, …

4. Writing the terms of the sequence

5. Writing Rules for Sequences
When the terms of a sequence have a recognizable pattern, you may be able to write a rule for the nth term of a sequence.
Describe pattern for -1, -8, -27, -64…

6. Example
You work in a grocery store and are stacking oranges in the shape of a square pyramid with seven layers. Write a rule for the number of oranges in each layer. Then graph the sequence.

7. Series and Summation Notation
When the terms of a sequence are added together, the resulting expression is a series. A series can be finite or infinite.
Finite Series:
Infinite Series: …

8. Series and Summation Notation
You can use summation notation to write a series. For example, the two series in the previous slide can be written in summation notation as follows.

9. Series and Summation Notation

10. Writing series using summation notation

11. Finding the Sum of a Series

12. Formulas for special series
These formulas can be proved with mathematical induction

13. Using a Formula for a Sum