SWBAT…write terms of an arithmetic sequence Tues, 4/17 Agenda 1. WU (10 min) 2. Notes on arithmetic sequences: 7 examples (35 min) Warm-Up: 1.Set up your Cornell notes. Topic is “Arithmetic Sequences.” 2.What pattern do you notice 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233,.... HW: Arithmetic Sequences

Fibonacci Sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233,...

 A sequence is a list of numbers that are related to each other by a rule.  The numbers in a sequence are called its terms. o The letter a with a subscript is used to represent the terms of a sequence. o a 1 represents the first term of the sequence o a 2 represents the second term of the sequence o a 3 represents the third term of the sequence, and so on  If the difference between successive terms is constant, then the sequence is called an arithmetic sequence.  The difference between consecutive terms is called the common difference, d, of the sequence.

To find the common difference (d), subtract any term from one that follows it

Example 1 Write the first six terms of the arithmetic sequence with the first term 6 and common difference 4. Solution 6, 10, 14, 18, 22, and 26

Example 2 Write the first six terms of the arithmetic sequence with a 1 = 5 and d = -2. Solution 5, 3, 1, -1, -3, and -5

Find the first term and the common difference of the arithmetic sequence. 34, 27, 20, 13, 6, -1, -8, … Solution: First term: 34 Common difference (d):= 27 – 34 = -7

The nth term of an arithmetic sequence with first term a 1 and common difference d is: The value of the term you are looking for First term The position the term is in The common difference

Find the eighth term of the arithmetic sequence whose first term is 4 and whose common difference is -7. Example 4 a 8 = 4 + (8 – 1)(-7) a 8 = 4 + (7)(-7) a 8 = -45 Check this result by writing the first eight terms of the sequence: a 8 = 4 + (-49) 4, -3, -10, -17, -24, -31, -38, -45

Find the 14 th term of the arithmetic sequence 4, 7, 10, 13,… Example 5

In the arithmetic sequence 4, 7, 10, 13,…, which term has a value of 301? Example 6

Find the formula for the nth term of the arithmetic sequence -7, -4, -1, 2… A. a n = 3n – 4 B. a n = -7n + 10 C. a n = 3n – 10 D. a n = -7n + 4 Example 7