# 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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