SWBATwrite terms of an arithmetic sequence Tues 417

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. 2 5 3 8 3 11 3 14 3

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, -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

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

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

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

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