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8.1 Defining and Using Sequences and Series

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Presentation on theme: "8.1 Defining and Using Sequences and Series"— Presentation transcript:

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


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