Algebra ii honors day 69
Download
1 / 29

Algebra II Honors—Day 69 - PowerPoint PPT Presentation


  • 73 Views
  • Uploaded on

Algebra II Honors—Day 69. Warmup. Solve and check: Find the next four terms of this arithmetic sequence: 207, 194, 181, . . . Find the indicated term of this arithmetic sequence:. Warmup. Check both solutions!!!. -13. -13. -13. -13. Warmup.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Algebra II Honors—Day 69' - remington-ronnie


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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Warmup
Warmup

  • Solve and check:

  • Find the next four terms of this arithmetic sequence:

    207, 194, 181, . . .

  • Find the indicated term of this arithmetic sequence:


Warmup1
Warmup

Check both solutions!!!


Warmup2

-13

-13

-13

-13

Warmup

  • Find the next four terms of this arithmetic sequence:

    207, 194, 181, . . .

    What is the common difference?? (194-207=-13 and 181-194=-13, so d=-13)

    207, 194, 181, 168, 155, 142, 129


Warmup3
Warmup

  • Find the indicated term of this arithmetic sequence:


Today
Today

Finish up Arithmetic Sequences and Series

Essential Question/New Material

Homework


Essential questions
Essential Questions

What is an arithmetic series and how is it calculated?

What is a geometric sequence?

What is a geometric series, and how is it calculated?


UPPER BOUND

(NUMBER)

SIGMA

(SUM OF TERMS)

NTH TERM

(SEQUENCE)

LOWER BOUND

(NUMBER)

n (Index of summation)

Sigma Notation


Definition:

Anarithmetic seriesis a series associated with an arithmetic sequence.

The sum of the first n terms:

OR


Examples:

Find the sum of the first 100 natural numbers.

1 + 2 + 3 + 4 + … + 100


Find the sum of the first 14 terms of the arithmetic series 2 + 5 + 8 + 11 + 14 + 17 +…

Examples:


Examples: 2 + 5 + 8 + 11 + 14 + 17 +…

Find the sum of the series


12.2 – Geometric Sequences and Series 2 + 5 + 8 + 11 + 14 + 17 +…


Arithmetic Series 2 + 5 + 8 + 11 + 14 + 17 +…

Geometric Series

Sum of Terms

Sum of Terms

Arithmetic Sequences

Geometric Sequences

ADD

To get next term

MULTIPLY

To get next term


Vocabulary of Sequences (Universal) 2 + 5 + 8 + 11 + 14 + 17 +…

ExplicitFormula

Recursive Formula:

an+1=an(r)


Find the next three terms of 2, 3, 9/2, ___, ___, ___ 2 + 5 + 8 + 11 + 14 + 17 +…

3 – 2 vs. 9/2 – 3… not arithmetic


1/2 2 + 5 + 8 + 11 + 14 + 17 +…

x

9

NA

2/3


The two geometric means are 6 and -18, since –2, 2 + 5 + 8 + 11 + 14 + 17 +…6, -18, 54

forms a geometric sequence

Find two geometric means between –2 and 54

-2, ____, ____, 54

-2

54

4

NA

x


-3, ____, ____, ____ 2 + 5 + 8 + 11 + 14 + 17 +…


x 2 + 5 + 8 + 11 + 14 + 17 +…

9

NA


x 2 + 5 + 8 + 11 + 14 + 17 +…

5

NA


*** Insert one geometric mean between ¼ and 4*** 2 + 5 + 8 + 11 + 14 + 17 +…

*** denotes trick question

1/4

3

NA


1/2 2 + 5 + 8 + 11 + 14 + 17 +…

7

x


Section 12.3 – Infinite Series 2 + 5 + 8 + 11 + 14 + 17 +…


Sequence 2 + 5 + 8 + 11 + 14 + 17 +…

Type

Series

1, 4, 7, 10, 13, ….

No Sum

Infinite Arithmetic

Finite Arithmetic

3, 7, 11, …, 51

Finite Geometric

1, 2, 4, …, 64

1, 2, 4, 8, …

Infinite Geometric

r > 1

r < -1

No Sum

Infinite Geometric

-1 < r < 1


Find the sum, if possible: 2 + 5 + 8 + 11 + 14 + 17 +…


Find the sum, if possible: 2 + 5 + 8 + 11 + 14 + 17 +…


Homework
Homework 2 + 5 + 8 + 11 + 14 + 17 +…

  • Handout on Arithmetic and Geometric Sequences/Series—Due Tuesday for a grade


ad