Standard and Learning Targets F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.*   SWBAT write arithmetic sequences explicitly SWBAT write arithmetic sequences recursively

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