8.1 Defining and Using Sequences and Series8.2 Analyzing Arithmetic Sequences and Series8.3 Analyzing Geometric Sequences and Series8.4 Finding Sums of Infinite Geometric Series8.5 Using Recursive Rules with Sequences8Sequences and SeriesMarching Band (p. 423)Skydiving (p. 431)Tree Farm (p. 449)Fish Population (p. 445)Museum Skylight (p. 416)Marching Band(p. 423)MuseumSkylight(p 416)()Tree Farm(p.449)Fi h Pl ti(445)SEE the Big IdeaChapter Learning Target:Understand sequences and series.Chapter Success Criteria:■I can define and use sequences and series.■I can describe how to find sums of infinite geometric series.■I can analyze arithmetic and geometric sequences and series.■I can explain how to write recursive rules for sequences.
407Maintaining Mathematical ProficiencyEvaluating FunctionsExample 1 Evaluate the function y=2x2−10 for the values x=0, 1, 2, 3, and 4.Input, x2x2−10Output, y02(0)2−10−1012(1)2−10−822(2)2−10−232(3)2−10842(4)2−1022Copy and complete the table to evaluate the function.1. y=3 −2x2. y=5x2+1 3. y=−4x +24xy123xy234xy51015Solving EquationsExample 2 Solve the equation 45=5(3)x.45 =5(3)xWrite original equation.45—5=5(3)x—5Divide each side by 5.9 =3xSimplify.log39 =log3 3xTake log3of each side.2 =xSimplify.Solve the equation. Check your solution(s).4. 7x+3 =31 5. 1—16=4 (1—2)x6. 216 =3(x+6)7. 2x+16 =144 8. 1—4x−8 =17 9. 8 (3—4)x=27—810. ABSTRACT REASONING The graph of the exponential decay function f(x) =bxhas an asymptote y=0. How is the graph of fdifferent from a scatter plot consisting of the points (1, b1), (2, b1+b2), (3, b1+b2 +b3), . . .? How is the graph of f similar?Dynamic Solutions available at BigIdeasMath.com
408Chapter 8Sequences and SeriesMathematical PracticesUsing Appropriate Tools StrategicallyMathematically proficient students consider the available tools when solving a mathematical problem.Monitoring ProgressUse a spreadsheet to help you answer the question.1. A pilot flies a plane at a speed of 500 miles per hour for 4 hours. Find the total distance flown at 30-minute intervals. Describe the pattern.2. A population of 60 rabbits increases by 25% each year for 8 years. Find the population at the end of each year. Describe the type of growth.3. An endangered population has 500 members. The population declines by 10% each decade for 80 years. Find the population at the end of each decade. Describe the type of decline.4. The top eight runners finishing a race receive cash prizes. First place receives $200, second place receives $175, third place receives $150, and so on. Find the fifth through eighth place prizes. Describe the type of decline.Using a SpreadsheetYou deposit $1000 in stocks that earn 15% interest compounded annually. Use a spreadsheet to find the balance at the end of each year for 8 years. Describe the type of growth.