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Algebra II Honors—Day 69PowerPoint Presentation

Algebra II Honors—Day 69

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Algebra II Honors—Day 69

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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

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

Warmup

- Find the indicated term of this arithmetic sequence:

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?

(NUMBER)

SIGMA

(SUM OF TERMS)

NTH TERM

(SEQUENCE)

LOWER BOUND

(NUMBER)

n (Index of summation)

Sigma Notation

Anarithmetic seriesis a series associated with an arithmetic sequence.

The sum of the first n terms:

OR

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

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 +…

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

*** denotes trick question

1/4

3

NA

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 2 + 5 + 8 + 11 + 14 + 17 +…

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