Precalculus: Sequences and Series Geometric Series

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True or False? A geometric series is the sum of the terms of an geometric sequence True

True
False
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Calculate the sum of the first 7 terms for the following geometric series: $$6 + 18 + 54 + ... $$

6558
6778
6989
7001
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Calculate the sum of the first 7 terms for the following geometric series: $$100 + 75 + 50 + ... $$

$$\frac{3175}{4}$$
$$\frac{3175}{64}$$
$$\frac{3175}{32}$$
$$\frac{3175}{16}$$
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Calculate the sum of the first 7 terms for the following geometric series: $$8 - 24 + 72 + ... $$

4376
4222
4132
4009
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Calculate the sum of the first 7 terms for the following geometric series: $$\frac{1}{3} + \frac{1}{6} + \frac{1}{12} + ... $$

$$\frac{71}{192}$$
$$\frac{127}{192}$$
$$\frac{127}{181}$$
$$\frac{192}{127}$$
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Calculate \(S_{6}\) for the following geometric series: $$6 + 30 + 150 + ...$$

19845
20001
23436
33458
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Calculate \(S_{6}\) for the following geometric series: $$-11 - 33 - 99 - ...$$

-2673
-2245
-2111
-2010
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Evaluate the sums for the following geometric series. $$1 + 6 + 36 + ... + 279936$$

302451
335923
384512
442254
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Evaluate the sums for the following geometric series. $$4 + 2 + 1 + ... + \frac{1}{1024}$$

$$\frac{8191}{512}$$
$$\frac{8191}{256}$$
$$\frac{8191}{3}$$
$$\frac{8191}{1024}$$
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A ball is dropped from a height of 3ft and bounces on the ground. At the top of each bounce, the ball reaches 60% of its previous height. Calculate the total distance travelled by the ball when it hits the ground for the fifth time.

9.5 m
10.8 m
11 m
16.7m
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