# Algebra II Honors—Day 69 - PowerPoint PPT Presentation

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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

### 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

• 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:

### Today

Finish up Arithmetic Sequences and Series

Essential Question/New Material

Homework

### 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:

Find the sum of the series

12.2 – Geometric Sequences and Series

Arithmetic Series

Geometric Series

Sum of Terms

Sum of Terms

Arithmetic Sequences

Geometric Sequences

To get next term

MULTIPLY

To get next term

Vocabulary of Sequences (Universal)

ExplicitFormula

Recursive Formula:

an+1=an(r)

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

3 – 2 vs. 9/2 – 3… not arithmetic

1/2

x

9

NA

2/3

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

-3, ____, ____, ____

x

9

NA

x

5

NA

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

*** denotes trick question

1/4

3

NA

1/2

7

x

Section 12.3 – Infinite Series

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

Find the sum, if possible:

Find the sum, if possible:

### Homework

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