Xa "Waiting for response fr X + edu.americanhighschool.org/dashboards/ActiveLearning/course-website.asp?action=assignment&Submitid=27111&srloid=271118rloid=27111&courseid=1486 = 72 American High School Cassidy Williams Dashboard * Management v 0 Reports UniLo. MVITA Checkpoint Apply Lessons Assessments % Unit 8: Mid Checkpoint Apply Unit 8: Inferences and Conclusions from Data Mid Checkpoint Apply Interactive Tools Unit 8: Inferences and Conclusions from Data Mid Checkpoint Apply Lesson 1 - 2 Algebra 2 Please complete the following questions. It is important that you show all work you did to solve the problems when you submit your work. This includes any calculations, diagrams, or graphs that helped you solve it. 1. OPEN ENDED Write an arithmetic series for which 55= 10. 2. OPEN ENDED Write a geometric series for which r= 1 and n = 4. 3. Writing in Math Use the information on page 649 to explain how arithmetic series apply to amphitheaters. Explain what the sequence and the series that can be formed from the given numbers represent, and show two ways to find the seating capacity of the amphitheater if it has ten rows of seats. 4. Writing in Math Use the information on page 663 to explain how e-mailing a joke is related to a geometric series. Include an explanation of how the situation could be changed to make it better to use a formula than to add terms. Your Answer ... Leave a message Type here to search g 7:32 PM 8/16/2017 19 X "Waiting for response from CC - Algebra 2 X + o { C intervisualtechnology.us/uploads/PDFs/ebooks/CC%20-%20Algebra%202/CC%20-%20Algebra%202 = 69. ACT/SAT What is the first term in the arithmetic sequence? American High School TTTTTTT A3 70. REVIEW The figures below show a pattern of filled leshiti circles that canesch 648 - 649 / 1100 relationship between 2 variables. OYO 0 Ooo OO a a оо Which rule relates to the number of wluite circles, to f, the number of dark cireles? F = 3/ H = 2/+1 GF=32-1 Main Ideas . Find sums of arithmetic series . Use signa notion 100% a C 10 Minimize D 11 New Vocabulary series arithmetic series sigma notation Index of summuti GET READY for the Lesson Austin, Texas has a strong musical tradition. It is home lo many indoor outdoor music venues where new and established musicians perform regularly Some of these venues are amphitheaters that generally get wider as the distance from the stage increases Suppose a section of an amphitheater can seat 18 people in the first row and each row can seat 4 more people than the previous row, Arithmetic Series The numbers of seats in the rows of the amphitheater form an arithmetic sequence. To find the number of people who could sit in the first four rows, add the first four terms of the sequence. That sum is 18 + 22 +26 + 30 or 96. A series is an indicated sum of the terms of a sequence. Since 18, 22, 26, 30 is an arithmetic sequence, 18 + 22 - 26 +30 is an arithmetic series. S represents the sum of the first w terms of a series. For example, is the sum of the first four terms. Study Tip * Spiral Review Find the exact solution(s) of each system of equations, lesson 11-7) 71. x + 2y = 33 72 ** + 2y = 33 x2 + y2 - 19 = 2x x2 - y2 - 9 Write each equation in standard form. State whether the graph of the equation is a parabala, circle, ellipse, or hyperbola. Then graph the equation. Les 10 73. y - 3x + 6y + 12 = 0 74. *? - 143 + 4 = 9y? -36y 75. If y varies directly as x and y = 5 when x = 2, find y when x = 6. fleson 4 Simplify each expression - 0 77. +3.14 78. 130 53 42774 Find all the zeros of each function, flesson 6) 79. x) = -32 +222 +21 80. y(x) = 12x + 42-32-3 81. SAVINGS Mackenzie has 557 in her bank account. She begins receiving a weekly allowance of $15, of which she deposits 20% in her bank account. Write an equation that represents how much money is in Mackenzie's account after x weeks. Leson2-4 GET READY for the Next Lesson PREREQUISITE SKILL Evaluate each expression for the given values of the variable. Lesson - 82. 3n-1,-1,2,3,4 85. 6-0 =1,2,3,4 84.4+7;m - 1,2,3,4,5 85. 4 - 2kk-3,4,5,6,7 Indicated Sum The sum of a series is the result when the terms of the series are added. An indicated Sun is the expression that ilustrates the Seris, which includes the term + - 76.39 39 To develop a formula for the sum of any arithmetic series, consider the series below. . S-4+ 11 +18 + 25 +32 +39 +46 +53 +60 Write Sy in two different orders and add the two equations. S = 4 + 11 + 18 + 25 + 32 +39 +46 +53 +60 (+) 5 = 60 +53 +46 +39 + 32 + 25 + 18 + 11 + 4 25-64 +64 +64 +64 +64 +64 +64 +64 +64 25-964) Note that the sum had 9 terms. 5:01) The sum of the first and last terms of the series is 61. An arithmetic series S, has n terms, and the sum of the first and last terms is + . Thus, the formula S. = 24 + .) represents the sum of any arithmetic series A O Type here to search g RERERE е سا 9 7:33 PM 8/16/2017 719 X "Waiting for response from CC - Algebra 2 o с intervisualtechnology.us/uploads/PDFs/ebooks/CC%20-%20Algebra%202/CC%20-%20Algebra%202 = 722 20 662 - 663 / 1100 American High School e sequences, the later the term in You may have noticed that in some describe this is the the sequence, the closer the value is as increases, approaches 0. The value that the terms of a sequence approach, in this case, is called the limit of the sequence. Other types of infinite sequences may also have limits. If the terms of a sequence do not approach a unique value, we say that the limit of the sequence does not exist. Main Ideas Hind sunod geometri . Find spects of geometric series GET READY for the Lesson 100% Suppose you e-mail a joke to three friends O friends sends the joke on to three of person who receives the joke on Tuesday sends it to three more people on Wednesday, and so on. New Vocabulary some series E-Mail Jokes DOX < ACTIVITY 1 Find the limit of the geometric sequence 1, 39. Step 1 Enter the sequence. • The formula for this sequence is = • Position the cursor on Ll in the STATEDIT Edit screen and enter the formula seq.N.N.1,10,1). This generates the values 1, 2...., 10 of the index N. • Position the cursor on L2 and enter the formula seql(1/3)^{N-1).N,1,10,1). This generates the first ten terms of the sequence KEYSTROKES: Review segniences in the Grupining Calculator Lab on page 632. Notice that as increases, the terms of the given sequence get closer and closer too. If you scroll down, you can see that for 2 & the terms are so close to that the calculator expresses them in scientific notation. This suggests that the limit of the sequence is O. Step 2 Graph the sequence. • Use a STAT PLOT to graph the sequence. Use ll as the list and L2 as the Ylist. KEYSTROKES: Review STAT PLOTS OR page 92 The graph also shows that, as n increases, the terms approach 0. In fact, for 26, the marks appear to lie on the horizontal axis. This strongly suggests that the limit of the sequence is 0. Geometric Series Notice that every day, the number of people who read your joke is three times the number that read it the day before. By Sunday, the number of people, including yourself, who have read the joke is 1+3+ 9 + 27 +81 +243 + 729 + 2187, or 3280! The numbers 1,3,4, 27, 41, 243,729, and 2187 form a geometric sequence in whicha Tandr 3. The indicated sum of the numbers in the sequence, 1+3+9+27 +81 +243 + 729 +2187, is called a geometric series >> To develop a formula for the sum of a geometrie series, consider the series given in the e-mail situation above. Multiply cach term in the series by the common ratio and subtract the result from the original series. S8 = 1 + 3+9+27 +81 +243 +229 +2157 (-)35 = 3+9+27+81 +243 +229 +2187 +6561 (1-3) = 1 + 0 + 0 + 0 + 0 + 0 + 0+ 0-6561 first term in series EXERCISES Use a graphing calculator to find the limit, if it exists, of each sequence. last term in series multiplied by common ratio; in this case, Study Tip Sy=1-3 or 3280 common ratio 1... =) 2.1=(-) 221 Terms of Geometric Sequences Remember that can also be written aan 5. a, = The expression for can be written as 5;="ITA rational expression like this can be used to find the sum of any geometric series A Type here to search g سا 7:34 PM 8/16/2017 719
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