2. Sequences Arithmetic Sequences Solving word problems. By Irma Crespo 2010

3. A Review Number of Sticks Number of Triangles 2 Triangles 5 Sticks 1 Triangle 3 Sticks 3 Triangles 7 Sticks 3, 5, 7, 9, 11, 13, 15,… A sequence is an ordered list of numbers. +2 An arithmetic sequence is a sequence with common difference. The difference is called the common difference.

4. 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.

5. 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? Oh,No! Oh,Yes! Word Problem Costs in $ Miles (m) 5.25 123 7.00 4 10.50 8.75 Costs of a Taxi Ride

6. Let’s Solve It Find the common difference. Costs in $ Miles (m) 5.25 123 7.00 4 10.508.75 +1.75 +1 The common difference is $1.75. The common difference is $1.75 times the miles (m). So, the expression is $1.75m. Wait!!! We are not done yet! Is the common difference the same as the cost in 1 mile? No.

7. Let’s Solve It How much can you add to $1.75 to get the cost at 1 mile, which is $5.25? We have $1.75m. Next, find a number you can add to the common difference that gives the cost at 1 mile. Costs in $ Miles (m) 5.25 123 7.00 4 10.508.75 $1.75 + ? = $5.25 $3.50 So, the expression is $1.75m + $3.50. And the cost at 9 miles is: ($1.75)(9) + $3.50 = $19.25

8. Week (n) Time Jogging (minutes) On the White Board If Luther continues the pattern shown in the table, how many minutes will he spend jogging each day during his 5 th week? 18 216 324 432 5? 40 Expression: 8n The 5 th week: 8(5) = 40 +1 +8

9. 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.

10. Time is up!

11. 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.