Unit 1 -Sequences and Series
Chapter 9 (pp 564 -609)
OBJECTIVES
Chapter 9 (pp 564 -609)
OBJECTIVES
- . Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments. ★
- Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
- . Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence
- For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key featuresinclude: intercepts; intervals where the function isincreasing, decreasing, positive, or negative; relative maximums and minimums;symmetries; end behavior; and periodicity. ★
- Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t , y = (0.97)t , y = (1.01) 12t, y = (1.2)t/10, and classify them asrepresenting exponential growth or decay.
- . Write a function that describes a relationship between two quantities. ★ a. Determine an explicit expression, a recursive process, or stepsfor calculation from a context. b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functionsto the model
- Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms
- Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
- . Interpret the parameters in a linear or exponential function in terms of a context.
Essential Questions
- What is a sequence?
- What is the difference in a recursive formula and and explicit formula?
- When is a sequence arithmetic?
- When is a sequence geometric?
- How is the sum of a finite algebraic series calculated?
- How is the sum of a finite geometric series calculated?
- Can the sum of an infinite geometric series be calculated? Explain.
- Can the sum of an infinite algebraic series be calculated? Explain.
- Explain convergence and divergence in a sequence.
- What is Fibonacci's sequence?
- Explain how the perfect spiral can be created.
- What is Phi?
TN Ready Standards
F-LE.A.2.
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
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TEXT- Arithmetic Sequences and Series
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VIDEO - ARITMETIC SEQUENCES
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Text- Geometric Sequences and Series Independent Practice
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VIDEO 1-
VIDEO 2- VIDEO 3-
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A-SSE.B.4.
Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.
Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.
F-IF A.3.
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.
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