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Precalculus: Sequences and Series Geometric Sequences
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True or False? A geometric sequence is a sequence where the ratios of the consecutive terms are constant
True
False
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State the general term for the following geometric sequence: 9, 36, 144, ...
$$t_n =7\times 4^{n-1}$$
$$t_n =9\times 4^{n-1}$$
$$t_n =9\times 2^{n-1}$$
$$t_n =9\times 4^{n+1}$$
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State the general term for the following geometric sequence: 625, 1250, 2500, ...
$$t_n =625\times 2^{n-1}$$
$$t_n =625\times 2^{n+1}$$
$$t_n =225\times 2^{n-1}$$
$$t_n =25\times 2^{n-1}$$
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State the general term for the following geometric sequence: 10125, 6750, 4500, ...
$$t_n =10125\times \bigg(\frac{4}{3}\bigg) ^{n-1}$$
$$t_n =10125\times \bigg(\frac{2}{3}\bigg) ^{n-1}$$
$$t_n =10125\times \bigg(\frac{1}{3}\bigg) ^{n-1}$$
$$t_n =10125\times \bigg(\frac{2}{3}\bigg) ^{n+1}$$
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Determine if the following sequence is arithmetic, geometric, or neither: 9, 13, 17, 21, ...
arithmetic
geometric
neither
none of the above
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Determine if the following sequence is arithmetic, geometric, or neither: 7, -21, 63, -189, ...
arithmetic
geometric
neither
none of the above
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Determine if the following sequence is arithmetic, geometric, or neither: 1, 11, 3, 167, ...
arithmetic
geometric
neither
none of the above
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State the first four terms for the following geometric sequence: $$t_n = 4^n$$
$$4, 16, 64, 256$$
$$2, 4, 8, 16$$
$$4, 16, 72, 256$$
$$4, 16, 24, 56$$
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Determine \(t_{6}\) for the following geometric sequence: $$896, 448, 224, ...$$
22
24
26
28
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Determine \(t_{6}\) for the following geometric sequence: $$6, 2, \frac{2}{3}, ...$$
$$\frac{2}{27}$$
$$\frac{1}{9}$$
$$\frac{1}{81}$$
$$\frac{2}{81}$$
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A certain antibiotic reduces the number of bacteria in your body by 10% each dose. If four doses of the antibiotic are taken, what percent of the original bacterial population is left?
65.61%
60.31%
75.22%
45.11%
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The 5th term of a geometric sequence is 45 and the 8th term is 360. What is the 29th term?
748941
256491
1474560
2156481
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Precalculus Playlist
19 Videos
01:50:07
103 Questions
0 Notes
The Basics
Functions and Relations
Classification of Numbers
Domain and Range
What is an Asymptote?
Radicals Review
Reflections
Intro to Exponential Functions
More on Trigonometry
Radians
Special Triangles
Determining if Triangles Exist
Ambiguous Case for Sine Law
Intro to Cycles, Periods, and Periodic Functions
Sequences and Series
What is a Recursive Formula
Arithmetic Sequences
Geometric Sequences
Arithmetic Series
Geometric Series
Simple Interest
Compound Interest