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12.1 – Arithmetic Sequences and Series. Arithmetic Series. Geometric Series. Sum of Terms. Sum of Terms. An introduction…………. Arithmetic Sequences. Geometric Sequences. ADD To get next term. MULTIPLY To get next term. Find the next four terms of –9, -2, 5, …. Arithmetic Sequence. - PowerPoint PPT Presentation

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12.1 Arithmetic Sequences and Series1An introduction

Arithmetic SequencesADDTo get next term

Geometric SequencesMULTIPLYTo get next termArithmetic SeriesSum of Terms

Geometric SeriesSum of Terms

2Find the next four terms of 9, -2, 5, Arithmetic Sequence

7 is referred to as the common difference (d)Common Difference (d) what we ADD to get next termNext four terms12, 19, 26, 333Find the next four terms of 0, 7, 14, Arithmetic Sequence, d = 721, 28, 35, 42Find the next four terms of x, 2x, 3x, Arithmetic Sequence, d = x4x, 5x, 6x, 7xFind the next four terms of 5k, -k, -7k, Arithmetic Sequence, d = -6k-13k, -19k, -25k, -32k4Vocabulary of Sequences (Universal)

5Given an arithmetic sequence with

x1538NA-3

X = 806

-1963??x6

353

7

Try this one:

1.516xNA0.5

8

9x633NA24

X = 279

-629 20NAx

10Find two arithmetic means between 4 and 5-4, ____, ____, 5

-445NAx

The two arithmetic means are 1 and 2, since 4, -1, 2, 5forms an arithmetic sequence11Find three arithmetic means between 1 and 41, ____, ____, ____, 4

154NAx

The three arithmetic means are 7/4, 10/4, and 13/4since 1, 7/4, 10/4, 13/4, 4 forms an arithmetic sequenceFind n for the series in which

5xy4403

X = 16Graph on positive window12.2 Geometric Sequences and Series14

Arithmetic SequencesADDTo get next term

Geometric SequencesMULTIPLYTo get next termArithmetic SeriesSum of Terms

Geometric SeriesSum of Terms

Vocabulary of Sequences (Universal)

Find the next three terms of 2, 3, 9/2, ___, ___, ___3 2 vs. 9/2 3 not arithmetic

17

1/2x9NA2/3

Find two geometric means between 2 and 54-2, ____, ____, 54

-2544NAx

The two geometric means are 6 and -18, since 2, 6, -18, 54forms an geometric sequence

-3, ____, ____, ____

x9NA

x5NA

*** Insert one geometric mean between and 4****** denotes trick question

1/43NA

1/27x

Section 12.3 Infinite Series1, 4, 7, 10, 13, .Infinite ArithmeticNo Sum3, 7, 11, , 51Finite Arithmetic

1, 2, 4, , 64Finite Geometric

1, 2, 4, 8, Infinite Geometricr > 1r < -1No Sum

Infinite Geometric-1 < r < 1

Find the sum, if possible:

Find the sum, if possible:

Find the sum, if possible:

Find the sum, if possible:

Find the sum, if possible:

The Bouncing Ball Problem Version AA ball is dropped from a height of 50 feet. It rebounds 4/5 ofits height, and continues this pattern until it stops. How fardoes the ball travel?50403232/5403232/5

The Bouncing Ball Problem Version BA ball is thrown 100 feet into the air. It rebounds 3/4 ofits height, and continues this pattern until it stops. How fardoes the ball travel?10075225/410075225/4

Sigma Notation

UPPER BOUND(NUMBER)LOWER BOUND(NUMBER)SIGMA(SUM OF TERMS)NTH TERM(SEQUENCE)

Rewrite using sigma notation: 3 + 6 + 9 + 12Arithmetic, d= 3

Rewrite using sigma notation: 16 + 8 + 4 + 2 + 1Geometric, r =

Rewrite using sigma notation: 19 + 18 + 16 + 12 + 4Not Arithmetic, Not Geometric

19 + 18 + 16 + 12 + 4 -1 -2 -4 -8Rewrite the following using sigma notation:

Numerator is geometric, r = 3Denominator is arithmetic d= 5 NUMERATOR:

DENOMINATOR:

SIGMA NOTATION: