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

The common difference is always the difference between any term and the term that proceeds that term. Common Difference = 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 any three of these we ought to be able to find the fourth.

Given: Find: IDENTIFY SOLVE

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

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

Given: Find: IDENTIFY SOLVE

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 NA -3 X = 80

Try this one: 1.5 16 x NA 0.5

9 x 633 NA 24 X = 27

-6 29 20 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