Questions and Answers
What is the initial value of the sequence represented by the points shown on the graph?
2
Which explicit function represents the geometric sequence of the heights of the bouncing toy?
Which graph is the sequence defined by the function f(x) = 3(2)^{x-1}?
Which is an equivalent representation of the function F(X) = 3/2(5/2) to determine the xth number in the sequence?
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What is the common ratio of the sequence -2, 6, -18, 54,...?
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Which graph represents a geometric sequence?
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What value should Lena use as the common ratio for the graphed geometric sequence?
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Which formula can be used to describe the sequence -81, 108, -144, 192,...?
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Which formula can be used to describe the sequence -2 2/3, -5 1/3, -10 2/3, -21 1/3, -42 2/3?
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What value should the conservationist use as the common ratio for the beach eroding at a rate of 1.1% each year?
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Study Notes
Geometric Sequences Overview
- Geometric sequences consist of numbers where each term is obtained by multiplying the previous term by a constant known as the common ratio.
- The initial value of a geometric sequence is critical for defining its starting point.
Initial Value
- The initial value of the sequence is 2.
Heights of a Bouncing Toy
- A bouncing toy's heights form a geometric sequence with terms of 64 inches, 48 inches, and 36 inches.
- The explicit function representing these heights is C.
Graph Representation
- The graph representing the sequence defined by the function f(x) = 3(2)^(x-1) corresponds to option D.
- Identifying graphs of geometric sequences is essential for visualizing their behavior.
Function Generation
- Pablo's function F(X) = 3/2(5/2) describes the xth term of a geometric sequence.
- An equivalent representation of this function is A.
Common Ratio
- The common ratio of the sequence -2, 6, -18, 54 is A.
Graph of Geometric Sequence
- Graph B represents a geometric sequence, distinguishing it from arithmetic sequences.
Common Ratio in Explicit Formula
- Lena computes the common ratio for her explicit formula as 2.5 based on the graphed geometric sequence.
Formula Descriptions
- The sequence -81, 108, -144, 192 can be described by formula C.
- Another sequence -2 2/3, -5 1/3, -10 2/3, -21 1/3, -42 2/3 can be described using formula D.
Beach Erosion
- A conservationist notes a beach erosion rate of 1.1% annually.
- The common ratio to use in the explicit formula for the remaining beach area is C.
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Description
This quiz covers the fundamentals of geometric sequences, including their initial value, common ratio, and how to graph them. It also discusses specific examples such as a bouncing toy's height and functions generated from sequences. Test your knowledge on the behavior and representation of geometric sequences.
