Questions and Answers
-81, 108, -144, 192,... Which formula can be used to describe the sequence?
f(x) = -81 (-4/3)^{x-1}
640, 160, 40, 10... Which correctly describe the graph of the geometric sequence? Select two options.
Natalia is writing a recursive formula to represent the sequence 8, 12, 18, 27,... What value should she use as the common ratio in the formula?
3/2
Isaak is writing an explicit formula to represent the sequence 64, 112, 196, 343,... What value should he use as the common ratio in the formula? Write the answer as a decimal rounded to the nearest hundredth.
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A conservationist determines that a particular beach is eroding at a rate of 1.1% each year. When writing an explicit formula to represent the amount of beach remaining each year, which value should she use as the common ratio?
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-2 2/3, -5 1/3, -10 2/3, -21 1/3, -42 2/3,... Which formula can be used to describe the sequence?
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A sequence of numbers begins with 12 and progresses geometrically. Each number is the previous number divided by 2. Which value can be used as the common ratio in an explicit formula that represents the sequence?
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Lena is asked to write an explicit formula for the graphed geometric sequence. What value, written as a decimal, should Lena use as the common ratio?
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The points shown on the graph represent the numbers in a geometric sequence. What is the initial value of the sequence?
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Which graph represents a geometric sequence?
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Study Notes
Geometric Sequences Key Points
- Sequence example: -81, 108, -144, 192 is described by the formula f(x) = -81 (-4/3)^(x-1).
- Sequence example: 640, 160, 40, 10 demonstrates exponential decay and has a domain of natural numbers.
Recursive and Explicit Formulas
- For the sequence 8, 12, 18, 27, Natalia should use a common ratio of 3/2 in her recursive formula.
- Isaak's explicit formula for the sequence 64, 112, 196, 343 requires a common ratio of 0.75 (0.75 rounded to two decimal places).
- A conservationist writing an explicit formula for beach erosion (1.1% per year) should use 0.989 as the common ratio.
Sequence Characteristics
- The sequence -2 2/3, -5 1/3, -10 2/3, -21 1/3, -42 2/3 can be modeled with the formula f(x+1) = 2f(x).
- A geometric sequence starting from 12 and divided by 2 has a common ratio of 1/2.
Graphical Representation
- Lena is tasked with finding an explicit formula for a graphed geometric sequence; her common ratio is 2.5.
- The initial value of a geometric sequence represented on a graph is 2.
- Graph representation for geometric sequences was found to be option B.
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Description
Test your knowledge on geometric sequences with this quiz! Explore various problems that include formulas, graphical representations, and recursive definitions. Perfect for students looking to sharpen their understanding of this important mathematical concept.
