1 / 14

11.1- Sequences and Series

11.1- Sequences and Series. Note: Remove 97-103o from tonight’s hw. Factorial Expressions. Simplify each expression. Introduction. What is a sequence? A sequence is an ordered list of numbers that follows a pattern.

agraff
Download Presentation

11.1- Sequences and Series

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 11.1- Sequences and Series Note: Remove 97-103o 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 ∑ 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

More Related