Arithmetic Sequences and Series

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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

Text of Arithmetic Sequences and Series

• Arithmetic Sequences and Series

• An introductionArithmetic SequencesADDTo get next termGeometric SequencesMULTIPLYTo get next term

• Find the next four terms of 9, -2, 5, Arithmetic Sequence7 is referred to as the common difference (d)Common Difference (d) what we ADD to get next termNext four terms12, 19, 26, 33

• Find 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, -32k

• Vocabulary of Sequences (Universal)

• Given an arithmetic sequence with x1538NA-3X = 80

• -1963??x6353

• Try this one:

• X = 27

• Find two arithmetic means between 4 and 5-4, ____, ____, 5-445NAx

• Find three arithmetic means between 1 and 41, ____, ____, ____, 4154NAx

• Find n for the series in which 5xy4403X = 16Graph on positive window

• Geometric Sequences and Series

• Arithmetic SequencesADDTo get next termGeometric SequencesMULTIPLYTo get next term

• Vocabulary of Sequences (Universal)

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

• 1/2x9NA2/3

• Find two geometric means between 2 and 54-2, ____, ____, 54-2544NAx

• -3, ____, ____, ____

• x9NA

• x5NA

• *** Insert one geometric mean between and 4****** denotes trick question1/43NA

• 1/27x

• Section 12.3 Infinite Series

• 1, 4, 7, 10, 13, .Infinite ArithmeticNo Sum3, 7, 11, , 51Finite Arithmetic1, 2, 4, , 64Finite Geometric1, 2, 4, 8, Infinite Geometricr > 1r < -1No SumInfinite 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?

• 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?

• Sigma Notation

• 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 Geometric19 + 18 + 16 + 12 + 4 -1 -2 -4 -8

• Rewrite the following using sigma notation:Numerator is geometric, r = 3Denominator is arithmetic d= 5 NUMERATOR:DENOMINATOR:SIGMA NOTATION:

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