Unit 5 – Series, Sequences, and Limits Section 5 Unit 5 – Series, Sequences, and Limits Section 5.1 – Arithmetic and Geometric Sequences Calculator Required

An introduction………… Arithmetic Series Sum of Terms Geometric Series Sum of Terms 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 7 is referred to as the common difference (d) Common Difference (d) – what we ADD to get next term Next four terms……12, 19, 26, 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, -32k

Vocabulary of Sequences (Universal)

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

Try this one: 1.5 16 x 0.5

9 x 633 24 X = 27

-6 29 20 x

Find two arithmetic means between –4 and 5 -4, ____, ____, 5 -4 5 4 x The two arithmetic means are –1 and 2, since –4, -1, 2, 5 forms an arithmetic sequence

Find three arithmetic means between 1 and 4 1, ____, ____, ____, 4 1 4 5 x The three arithmetic means are 7/4, 10/4, and 13/4 since 1, 7/4, 10/4, 13/4, 4 forms an arithmetic sequence

Vocabulary of Sequences (Geometric)

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

1/2 x 9 2/3

Find two geometric means between –2 and 54 -2, ____, ____, 54 -2 54 4 x The two geometric means are 6 and -18, since –2, 6, -18, 54 forms an geometric sequence

-3, ____, ____, ____

x 9

x 5

*** Insert one geometric mean between ¼ and 4*** 1/4 3