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Course 3 13-1 Terms of Arithmetic Sequences 13-1 Terms of Arithmetic Sequences Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

# Course 3 13-1 Terms of Arithmetic Sequences 13-1 Terms of Arithmetic Sequences Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation

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### Text of Course 3 13-1 Terms of Arithmetic Sequences 13-1 Terms of Arithmetic Sequences Course 3 Warm Up Warm...

• Warm UpProblem of the DayLesson Presentation

• Warm UpFind the next two numbers in the pattern, using the simplest rule you can find.

1. 1, 5, 9, 13, . . .2. 100, 50, 25, 12.5, . . .3. 80, 87, 94, 101, . . .4. 3, 9, 7, 13, 11, . . .17, 216.25, 3.125108, 11517, 15

• Problem of the Day

Write the last part of this set of equations so that its graph is the letter W.y = 2x + 4 for 0 x 2y = 2x 4 for 2 < x 4y = 2x + 12 for 4 < x 6Possible answer: y = 2x 12 for 6 < x 8

• Learn to find terms in an arithmetic sequence.

• Determine if the sequence could be arithmetic. If so, give the common difference.5, 8, 11, 14, 17, . . .Additional Example 1A: Identifying Arithmetic SequencesThe terms increase by 3.The sequence could be arithmetic with a common difference of 3.5 8 11 14 17, . . .3333

• Determine if the sequence could be arithmetic. If so, give the common difference.1, 3, 6, 10, 15, . . .Additional Example 1B: Identifying Arithmetic Sequences The sequence is not arithmetic.Find the difference of each term and the term before it.1 3 6 10 15, . . .5432

• Determine if the sequence could be arithmetic. If so, give the common difference.65, 60, 55, 50, 45, . . .Additional Example 1C: Identifying Arithmetic Sequences The sequence could be arithmetic with a common difference of 5.The terms decrease by 5.65 60 55 50 45, . . .5555

• Determine if the sequence could be arithmetic. If so, give the common difference.5.7, 5.8, 5.9, 6, 6.1, . . .Additional Example 1D: Identifying Arithmetic SequencesThe sequence could be arithmetic with a common difference of 0.1.The terms increase by 0.1.5.7 5.8 5.9 6 6.1, . . .0.10.10.10.1

• Determine if the sequence could be arithmetic. If so, give the common difference.1, 0, -1, 0, 1, . . .Additional Example 1E: Identifying Arithmetic SequencesThe sequence is not arithmetic.Find the difference of each term and the term before it.1 0 1 0 1, . . .1111

• Determine if the sequence could be arithmetic. If so, give the common difference.1, 2, 3, 4, 5, . . .Check It Out: Example 1AThe sequence could be arithmetic with a common difference of 1.The terms increase by 1.1 2 3 4 5, . . .1111

• Determine if the sequence could be arithmetic. If so, give the common difference.1, 3, 7, 8, 12, Check It Out: Example 1BThe sequence is not arithmetic.Find the difference of each term and the term before it.1 3 7 8 12, . . .4142

• Determine if the sequence could be arithmetic. If so, give the common difference.11, 22, 33, 44, 55, . . .Check It Out: Example 1CThe sequence could be arithmetic with a common difference of 11.The terms increase by 11.11 22 33 44 55, . . .11111111

• Determine if the sequence could be arithmetic. If so, give the common difference.1, 1, 1, 1, 1, 1, . . .Check It Out: Example 1DThe sequence could be arithmetic with a common difference of 0.Find the difference of each term and the term before it.1 1 1 1 1, . . .0000

• Determine if the sequence could be arithmetic. If so, give the common difference.2, 4, 6, 8, 9, . . .Check It Out: Example 1EThe sequence is not arithmetic.Find the difference of each term and the term before it.2 4 6 8 9, . . .1222

• Find the given term in the arithmetic sequence.10th term: 1, 3, 5, 7, . . .Additional Example 2A: Finding a Given Term of an Arithmetic Sequencean = a1 + (n 1)da10 = 1 + (10 1)2a10 = 19

• Find the given term in the arithmetic sequence.18th term: 100, 93, 86, 79, . . .Additional Example 2B: Finding a Given Term of an Arithmetic Sequencean = a1 + (n 1)da18 = 100 + (18 1)(7)a18 = -19

• Find the given term in the arithmetic sequence.21st term: 25, 25.5, 26, 26.5, . . .Additional Example 2C: Finding a Given Term of an Arithmetic Sequencean = a1 + (n 1)da21 = 25 + (21 1)(0.5)a21 = 35

• Find the given term in the arithmetic sequence.14th term: a1 = 13, d = 5Additional Example 2D: Finding a Given Term of an Arithmetic Sequencean = a1 + (n 1)da14 = 13 + (14 1)5a14 = 78

• Find the given term in the arithmetic sequence.15th term: 1, 3, 5, 7, . . .Check it Out: Example 2Aan = a1 + (n 1)da15 = 1 + (15 1)2a15 = 29

• Find the given term in the arithmetic sequence.50th term: 100, 93, 86, 79, . . .Check It Out: Example 2Ban = a1 + (n 1)da50 = 100 + (50 1)(-7)a50 = 243

• Find the given term in the arithmetic sequence.41st term: 25, 25.5, 26, 26.5, . . .Check It Out: Example 2Can = a1 + (n 1)da41 = 25 + (41 1)(0.5)a41 = 45

• Find the given term in the arithmetic sequence.2nd term: a1 = 13, d = 5Check It Out: Example 2Dan = a1 + (n 1)da2 = 13 + (2 1)5a2 = 18

• You can use the formula for the nth term of an arithmetic sequence to solve for other variables.

• The senior class held a bake sale. At the beginning of the sale, there was \$20 in the cash box. Each item in the sale cost 50 cents. At the end of the sale, there was \$63.50 in the cash box. How many items were sold during the bake sale?Additional Example 3: ApplicationIdentify the arithmetic sequence: 20.5, 21, 21.5, 22, . . .a1 = 20.5a1 = 20.5 = money after first saled = 0.5an = 63.5d = .50 = common differencean = 63.5 = money at the end of the sale

• Additional Example 3 ContinuedLet n represent the item number of cookies sold that will earn the class a total of \$63.50. Use the formula for arithmetic sequences.an = a1 + (n 1) dSolve for n.63.5 = 20.5 + (n 1)(0.5)63.5 = 20.5 + 0.5n 0.5Distributive Property.63.5 = 20 + 0.5nCombine like terms.87 = nSubtract 20 from both sides.During the bake sale, 87 items are sold in order for the cash box to contain \$63.50.43.5 = 0.5nDivide both sides by 0.5.

• Johnnie is selling pencils for student council. At the beginning of the day, there was \$10 in his money bag. Each pencil costs 25 cents. At the end of the day, he had \$40 in his money bag. How many pencils were sold during the day?Check It Out: Example 3Identify the arithmetic sequence: 10.25, 10.5, 10.75, 11, a1 = 10.25d = 0.25an = 40a1 = 10.25 = money after first saled = .25 = common differencean = 40 = money at the end of the sale

• Check It Out: Example 3 ContinuedLet n represent the number of pencils in which he will have \$40 in his money bag. Use the formula for arithmetic sequences.an = a1 + (n 1)dSolve for n.40 = 10.25 + (n 1)(0.25)40 = 10.25 + 0.25n 0.25Distributive Property.40 = 10 + 0.25nCombine like terms.120 = nSubtract 10 from both sides.120 pencils are sold in order for his money bag to contain \$40.30 = 0.25nDivide both sides by 0.25.

• Lesson QuizDetermine if each sequence could be arithmetic. If so, give the common difference.1. 42, 49, 56, 63, 70, . . . 2. 1, 2, 4, 8, 16, 32, . . .Find the given term in each arithmetic sequence.3. 15th term: a1 = 7, d = 54. 24th term: 1, , , , 25. 52nd term: a1 = 14.2; d = 1.2noyes; 77747

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