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Sequences Arithmetic Sequences Solving word problems. By Irma Crespo 2010 A Review • A sequence is an ordered list of numbers. 1 Triangle 2 Triangles 3 Triangles 3 Sticks 5 Sticks 7 Sticks Number of Triangles Number of Sticks • 3, 5, 7, 9, 11, 13, 15,… +2 +2 +2 +2 +2 +2 The difference is called the common difference. • An arithmetic sequence is a sequence with common difference. Remember Our Easy Tricks • Only think addition to get the next term. • Common difference means the terms in a sequence are either increasing or decreasing at the same amount. • If term 1 and the common difference are the same, the expression is common difference times the term number (n). • If term 1 and the common difference are NOT the same, the expression consists of the common difference times the term number (n) and the number added to the common difference to get the first term. The expression should be in this order. Oh,No! Oh,Yes! Word Problem • The cost of a taxi ride for 1,2,3, and 4 miles are shown in this arithmetic sequence. What would be the cost of a 9-mile ride? Costs of a Taxi Ride Miles (m) Costs in $ 1 2 3 4 5.25 7.00 8.75 10.50 Let’s Solve It • Find the common difference. +1 Miles (m) Costs in $ +1 +1 1 2 3 5.25 7.00 8.75 +1.75 +1.75 4 10.50 Wait!!! +1.75 We are not done yet! The common difference is $1.75. The common difference is $1.75 times the miles (m). So, the expression is $1.75m. Is the common difference the same as the cost in 1 mile? No. Let’s Solve It • We have $1.75m. Next, find a number you can add to the common difference that gives the cost at 1 mile. Miles (m) Costs in $ 1 2 3 4 5.25 7.00 8.75 10.50 How much can you add to $1.75 to get the cost at 1 mile, which is $5.25? $1.75 + $3.50 ? = $5.25 • So, the expression is $1.75m + $3.50. • And the cost at 9 miles is: ($1.75)(9) + $3.50 = $19.25 On the White Board • If Luther continues the pattern shown in the table, how many minutes will he spend jogging each day during his 5th week? Week (n) Time Jogging 1 2 3 4 5 8 16 24 32 4?0 (minutes) Expression: 8n The 5th week: 8(5) = 40 Practice, Practice,Practice • Complete the worksheet. • You have a choice to work on your own or to work with a partner. • Completed worksheets are submitted for grading. • Solutions are discussed the next day. Time is up! Main Resources LINEAR FUNCTIONS (Chapter 9) LESSON PLAN by • Math Connects: Concepts, Skills, and Problem Solving Teacher Edition; Course 3, Volume 2 Columbus:McGraw-Hill, 2009. POWERPOINT CREATED by • Irma Crespo. University of Michigan-Dearborn, School of Education; Winter, 2010.