1. For f(4) 2. For f(-3) 3. For f(-9) Warm-Up Evaluate the following: Have students recall how to solve 3. For f(-9)

How do we write the function to represent a sequence? GSE Alg I Support UNIT QUESTION: How do we graph functions, and what can be done to change the way they look? Standard: MM1A1 Today’s Question: How do we write the function to represent a sequence? Standard: MM1A1f

Sequences Everyday a radio station asks a question for a prize of $150. If the fifth caller does not answer correctly, the prize money increased by $150 each day until someone correctly answers their question. Make a list of the prize money for a week from Monday to Friday if no one gets it right.

Contest Monday: $150 Tuesday: $300 Wednesday: $450 Thursday: $600 Friday: $750

Sequences These prize amounts form a sequence. Sequence: A function whose domain is a set of consecutive whole numbers.

Sequences The values in the range are called the terms of the sequence. Domain: 1 2 3 4…....n Range: a1 a2 a3 a4….. an A sequence can be specified by an equation or rule.

Contest a1 $150 a2 $300 a3 $450 a4 $600 a5 $750 an represents a general term where n can be any number. What is the closed formula for an?

Sequences Sequences can continue forever. We can calculate as many terms as we want as long as we know the rule or equation for an. Example: 2, 8, 14, 20, ___ , ___,……. _____ . an = 6n - 4

Writing Terms of a Sequence an = 2n – 3 Find a1, a2, a3, a4, a5 a1 = -1 First Term a2 = 1 Second Term a3 = 3 Third Term a4 = 5 Fourth Term a5 = 7 Fifth Term

Practice an = -5n + 20 Find a1, a2, a3, a4, a5 a1 = First Term a2 = Second Term a3 = Third Term a4 = Fourth Term a5 = Fifth Term 15 10 5 -5

Arithmetic Sequences

Writing Rules Using the Formula: an = a1+ d(n-1) a1 = 3 First Term a2 = 5 Second Term a3 = 7 Third Term a4 = 9 Fourth Term an = nth Term What is the rule? an = ??? an= 3 + 2(n-1) an= 3 + 2n – 2 = 2n + 1

Writing Rules for a Sequence a1 = 2 First Term a2 = 6 Second Term a3 = 10 Third Term a4 = 14 Fourth Term an = nth Term What is the rule? an = ??? an= 4n - 2

Writing Rules for a Sequence a1 = 7 First Term a2 = 4 Second Term a3 = 1 Third Term a4 = -2 Fourth Term an = ?? nth Term What is the rule? an = ???

Try This! a1 = 5 First Term a2 = 12 Second Term a3 = 19 Third Term a4 = 26 Fourth Term an = nth Term What is the rule? an = ??? an= 7n - 2

EOCT Practice 77 b) 81 c) 84 d) 86 b

EOCT Practice Find the 25th term of the sequence 7, 11, 15, 19, 23, ... 103 b) 104 c) 107 d) 111 a

Practice Sequence Worksheet Homework Practice Sequence Worksheet