big ideas - algebra 2 - chapter 8.pdf - 8 8.1 8.2 8.3 8.4 8.5 Sequences and Series Defining and Using Sequences and Series Analyzing Arithmetic

# big ideas - algebra 2 - chapter 8.pdf - 8 8.1 8.2 8.3 8.4...

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8.1 Defining and Using Sequences and Series 8.2 Analyzing Arithmetic Sequences and Series 8.3 Analyzing Geometric Sequences and Series 8.4 Finding Sums of Infinite Geometric Series 8.5 Using Recursive Rules with Sequences 8 Sequences and Series Marching Band (p. 423) Skydiving (p. 431) Tree Farm (p. 449) Fish Population (p. 445) Museum Skylight (p. 416) Ma rc hi ng B an d (p . 423) Mu seum Skyligh t (p 416) ( ) Tree Farm (p . 449) Fi h P l ti ( 445) SEE the Big Idea Chapter 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.
407 Maintaining Mathematical Proficiency Evaluating Functions Example 1 Evaluate the function y = 2 x 2 10 for the values x = 0, 1, 2, 3, and 4. Input, x 2 x 2 10 Output, y 0 2( 0 ) 2 10 10 1 2( 1 ) 2 10 8 2 2( 2 ) 2 10 2 3 2( 3 ) 2 10 8 4 2( 4 ) 2 10 22 Copy and complete the table to evaluate the function. 1. y = 3 2 x 2. y = 5 x 2 + 1 3. y = 4 x + 24 x y 1 2 3 x y 2 3 4 x y 5 10 15 Solving Equations Example 2 Solve the equation 45 = 5(3) x . 45 = 5(3) x Write original equation. 45 5 = 5(3) x 5 Divide each side by 5. 9 = 3 x Simplify. log 3 9 = log 3 3 x Take log 3 of each side. 2 = x Simplify. Solve the equation. Check your solution(s). 4. 7 x + 3 = 31 5. 1 16 = 4 ( 1 2 ) x 6. 216 = 3( x + 6) 7. 2 x + 16 = 144 8. 1 4 x 8 = 17 9. 8 ( 3 4 ) x = 27 8 10. ABSTRACT REASONING The graph of the exponential decay function f ( x ) = b x has an asymptote  y   = 0. How is the graph of f different from a scatter plot consisting of the points (1,  b 1 ), (2, b 1 + b 2 ), (3, b 1 + b 2 + b 3 ), . . .? How is the graph of f similar? Dynamic Solutions available at BigIdeasMath.com