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70 = ( + ) 2 15 5 Math Lab Notes and Solutions 2. n = 7; the pyramid cannot be built because the common difference is not a whole number and therefore cannot be represented by a penny. 3. 70 = n 2 (20 + 8); n = 5; the common difference is 3. The arithmetic sequence is 20, 17, 14, 11, 8. 4. 90 = n 2 (18 + 12); n = 6; the pyramid cannot be built because the common difference is not a whole number and therefore cannot be represented by a penny. MATH LAB Activity 2 PREPARE • This lab is interactive and intuitive. Be sure that each group has a roll of pennies. TEACH • Students should work in groups of 3 students. • Roles for students are as follows: 1. recorder 2. pyramid builder 3. calculator • Students will have to build the pyramids and test for common differences in Steps 2, 3, and 4. FOLLOW-UP • As a class, discuss the applications of this type of situation. If anyone in the class has worked in a store and had experience building displays, invite them to share their experiences. • Discuss the advantages to calculating before you start to build and the results in you begin building before you know the number of rows, the starting number in the row, the ending number in the row, and the common difference. Math Labs 421
Math Applications Solutions and Notes 1. a. 28 – 21 = 7 28 + 7 + 1 = 36 b. Calculate the difference between the last two terms and then add 1. Add the result to the last term in the sequence to find the next term in the sequence. c. n 3 = (n 2 – n 1 + 1) + n 2 = 2n 2 – n 1 + 1 2. a. 2 0 , 2 1 , 2 2 , and 2 3 b. Let the row number equal n. n – 1 = 8 n = 9 or 9th row c. 2 8 = 1 + 8 + 28 + 56 + 70 + 56 + 28 + 8 + 1 = 256 422 Chapter 9 Sequences and Series
Page 1 and 2: LESSON OBJECTIVES 9.1 Patterns •
Page 3 and 4: LESSON PLANNING Vocabulary sequence
Page 5 and 6: INSTRUCTION Example 2 Return to the
Page 7 and 8: Answers to Math Applications Math A
Page 9 and 10: INSTRUCTION Tell students that the
Page 11 and 12: INSTRUCTION Ongoing Assessment Show
Page 15 and 16: INSTRUCTION Tell students that the
Page 17 and 18: Problem Solving Before solving this
Page 21 and 22: INSTRUCTION Students might incorrec
Page 23 and 24: WRAP UP To ensure mastery of object
Page 25 and 26: Mixed Review Additional Answers 35.
Page 27 and 28: INSTRUCTION Ask students to express
Page 29 and 30: WRAP UP To ensure mastery of object
Page 31: MATH LAB Activity 1 PREPARE • An
Page 35 and 36: Math Applications Solutions and Not
Page 41 and 42: Vocabulary Review arithmetic mean (
Page 43 and 44: 1 2 10 , 922 1 2 ∞ 1 ∑

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