Arithmetic Sequences An Arithmetic Sequence is defined as

Arithmetic Sequences

An Arithmetic Sequence is defined as a sequence in which there is a common difference between consecutive terms.

Which of the following sequences are arithmetic? Identify the common difference. YES NO NO YES

e c n e r e f f i d n The commo e h t s y a w l a is y n a n e e w t e b e c n e r e f f di t a h t m r e term and th. m r e t t a h t s proceed Comm on Differe nce = 5

The general form of an ARITHMETIC sequence. First Term: Second Term: Third Term: Fourth Term: Fifth Term: nth Term:

Formula for the nth term of an ARITHMETIC sequence. If we know three any o ough f these we t to b to fin e ab le d the fourt h.

Given: Find: IDENTIFY SOLVE

Given: Find: What term number is -169? IDENTIFY SOLVE

Given: What’s the real question? IDENTIFY Find: The Difference SOLVE

Given: IDENTIFY Find: SOLVE

An introduction………… Arithmetic Sequences Geometric Sequences ADD To get next term MULTIPLY To get next term Arithmetic Series Geometric Series Sum of Terms

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, 2 x, 3 x, … Arithmetic Sequence, d = x 4 x, 5 x, 6 x, 7 x Find the next four terms of 5 k, -7 k, … Arithmetic Sequence, d = -6 k -13 k, -19 k, -25 k, -32 k

Vocabulary of Sequences (Universal)

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

Try this one: 1. 5 x 16 NA 0. 5

9 633 x NA 24 X = 27

-6 20 29 NA x

Find two arithmetic means between – 4 and 5 -4, ____, 5 -4 5 4 NA 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 NA 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