Silent Do Now (5 minutes) Silent Do Now (5 minutes) * Before you begin, take out your homework (worksheet from last class) Find the rate of change between (3,2) and (4,6). There is a relationship between the number of the shape and the number of sides. Find the next shape in the sequence.

Agenda Review Do Now Track Exit Tickets Lesson on Sequences Independent Practice Exit Ticket

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. Fill out the chart on your paper accordingly!

Contest Monday: $150 Tuesday: $300 Wednesday: $450 Thursday: $600 Friday: $750 These prize amounts form a sequence.

Important Definitions Sequence: A function whose domain is a set of consecutive whole numbers. It can be specified by an equation or a rule. Arithmetic Sequence: a sequence that has a constant common difference.

Important Definitions (ctd.) The values in the range are called the terms of the sequence. Domain: 1 2 3 4…....n Range: a1 a2 a3 a4….. An

Contest a1 $150 a2 $300 Sequences can continue forever. We can calculate as many terms as we want as long as we know the rule or equation for an. a3 $450 a4 $600 a5 $750 an represents a general term where n can be any number.

Example 1: Given the rule an = 6n – 4 , find the next term in the sequence. 2, 8, 14, 20, ___ ,___.

Quick Check

#1 Review 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

#2 Review 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 Explicit Formula Recursive Formula an = an-1 + d

Example 2: Write the rule for the nth term in the sequence 2, 6, 10, 14, Identify the first term: Identify the common difference between each of the values: Write the rule:

Review #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

Review #2 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

Review #3 a1 = 7 First Term a2 = 4 Second Term a3 = 1 Third Term a4 = -2 Fourth Term an = ?? nth Term What is the rule? an = ???

Example 3: Find a specific term in a sequence Find the 21st term in the sequence by writing a rule. 1, 10, 19, 28

Quick Check!

Independent Practice

Exit Ticket 1. Given the sequence: 3, 7, 11, 15, 19 Find the explicit formula for the nth term Find the recursive formula. Find the next two terms in the sequence 2. Find the 20th term in the sequence: an = 4n - 5