Algebra ii honors day 69
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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.

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Algebra II Honors—Day 69

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Algebra ii honors day 69

Algebra II Honors—Day 69


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?


Algebra ii honors day 69

UPPER BOUND

(NUMBER)

SIGMA

(SUM OF TERMS)

NTH TERM

(SEQUENCE)

LOWER BOUND

(NUMBER)

n (Index of summation)

Sigma Notation


Algebra ii honors day 69

Definition:

Anarithmetic seriesis a series associated with an arithmetic sequence.

The sum of the first n terms:

OR


Algebra ii honors day 69

Examples:

Find the sum of the first 100 natural numbers.

1 + 2 + 3 + 4 + … + 100


Algebra ii honors day 69

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

Examples:


Algebra ii honors day 69

Examples:

Find the sum of the series


Algebra ii honors day 69

12.2 – Geometric Sequences and Series


Algebra ii honors day 69

Arithmetic Series

Geometric Series

Sum of Terms

Sum of Terms

Arithmetic Sequences

Geometric Sequences

ADD

To get next term

MULTIPLY

To get next term


Algebra ii honors day 69

Vocabulary of Sequences (Universal)

ExplicitFormula

Recursive Formula:

an+1=an(r)


Algebra ii honors day 69

Find the next three terms of 2, 3, 9/2, ___, ___, ___

3 – 2 vs. 9/2 – 3… not arithmetic


Algebra ii honors day 69

1/2

x

9

NA

2/3


Algebra ii honors day 69

The two geometric means are 6 and -18, since –2, 6, -18, 54

forms a geometric sequence

Find two geometric means between –2 and 54

-2, ____, ____, 54

-2

54

4

NA

x


Algebra ii honors day 69

-3, ____, ____, ____


Algebra ii honors day 69

x

9

NA


Algebra ii honors day 69

x

5

NA


Algebra ii honors day 69

*** Insert one geometric mean between ¼ and 4***

*** denotes trick question

1/4

3

NA


Algebra ii honors day 69

1/2

7

x


Algebra ii honors day 69

Section 12.3 – Infinite Series


Algebra ii honors day 69

Sequence

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


Algebra ii honors day 69

Find the sum, if possible:


Algebra ii honors day 69

Find the sum, if possible:


Homework

Homework

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


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