Unit 3A Expressions Lesson 2 Sequences

Lesson 2: Sequences Objective: Swbat find the terms of an arithmetic sequence. Do Now: Worksheet

Lesson 2: Sequences Definitions A sequence is an ordered list of numbers. Each number in a sequence is called a term. In an arithmetic sequence, each term is found by adding the same number to the previous term.

Lesson 2: Sequences In an arithmetic sequence, the terms can be whole numbers, fractions or decimals. Describe the relationship between terms and write the next three terms. a.) 1,3,5,7,9, _____, _____, _____ b.) 1, 1.5, 2, 2.5, _____, _____, _____ c.) 45, 42, 39, _____, _____, _____

Lesson 2: Sequences In an arithmetic sequence, the terms can be whole numbers, fractions or decimals. Describe the relationship between terms and write the next three terms. a.) 1, 3, 5, 7, 9, 11, 13, 15 add 2 b.) 1, 1.5, 2, 2.5, _____, _____, _____ c.) 45, 42, 39, _____, _____, _____

Lesson 2: Sequences In an arithmetic sequence, the terms can be whole numbers, fractions or decimals. Describe the relationship between terms and write the next three terms. a.) 1, 3, 5, 7, 9, 11, 13, 15 add 2 b.) 1, 1.5, 2, 2.5, 3, 3.5, 4 add .5 c.) 45, 42, 39, _____, _____, _____

Lesson 2: Sequences In an arithmetic sequence, the terms can be whole numbers, fractions or decimals. Describe the relationship between terms and write the next three terms. a.) 1, 3, 5, 7, 9, 11, 13, 15 add 2 b.) 1, 1.5, 2, 2.5, 3, 3.5, 4 add .5 c.) 45, 42, 39, 36, 33, 30 add -3

Lesson 2: Sequences Describe the relationship and find the next three terms: 8, 13, 18, 23…. .4, .6, .8, 1 … 0, 13, 26, 39… 4, 7, 10, 13… 1.0, 1.3, 1.6, 1.9…

Lesson 2: Sequences In a sequence, each term has a specific position within the sequence. You can write an algebraic Expression to find the nth term of the sequence. Term 1st 2nd 3rd 4th nth Sequence 4, 8, 12, 16 ___ +4 and if same y/x then you can write Algebraic Expression: 4n

Lesson 2: Sequences Real-World Example The number of students who went on each horseback riding trip is shown. Do the numbers represent the terms of an arithmetic sequence? Explain. Trip 1 2 3 4 5 Number of Students 15 16 18 21 25

Lesson 2: Sequences Example 1: The greeting cards that Mary makes are sold in boxes at a gift store. The first week, the store sold 5 boxes. Each week, the store sells 5 more boxes. The pattern continues. Write an algebraic expression and find the total number of boxes sold at the end of the 100th week.

Lesson 2: Sequences Example 2: If the pattern continues, what algebraic expression can be used to find the number of circles used in any figure. How many circles will be in the 50th figure? Figure (x) 1 2 3 n Circles (y) 3 6 9 ___

Classwork Guided Practice #1 – 5 Independent Practice #1 – 8 Problem Solving #1 - 8

Closure Question: What is an arithmetic sequence? Exit Ticket Homework: Practice # 1 - 17

Exit Ticket Given the sequence 8, 16, 24, 32, …. Write an algebraic expression: ______________ Find the 9th term of the sequence: __________

Homework