62 – Arithmetic and Geometric Sequences Calculator Required

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Presentation transcript:

62 – Arithmetic and Geometric Sequences Calculator Required Sequences and Series Investigations 62 – Arithmetic and Geometric Sequences Calculator Required

An introduction………… Arithmetic Sequences Geometric Sequences ADD To get next term MULTIPLY To get next term Let’s focus on arithmetic sequences first.

What is added to get the next term is called the common difference (d) Arithmetic Sequences What is added to get the next term is called the common difference (d) ADD To get next term d = 3 d = –8 d = 0.4 d = 3 Note: The common difference is what is added to get the next term….even if negative.

Find the next four terms of –9, –2, 5, … Arithmetic Sequence Next four terms…… 5 + 7 = 12 12 + 7 = 19 19 + 7 = 26 26 + 7 = 33

Find the next four terms of 0, 7, 14, … Arithmetic Sequence, d = 7 21, 28, 35, 42 Find the next four terms of x, 2x, 3x, … Arithmetic Sequence, d = x 4x, 5x, 6x, 7x Find the next four terms of 5k, -k, -7k, … Arithmetic Sequence, d = -6k -13k, -19k, -25k, -31k

Vocabulary of Arithmetic Sequences (also universal)

Given an arithmetic sequence with x 38 15 -3 x = 80

1.5 x 16 0.5

9 633 x 24 x = 27

-6 29 20 x

Vocabulary of Sequences (Geometric)

x 9

-3, ____, ____, ____

x 9

x 5