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Test: Geometric Series - Ambitious

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Question 1: Which of the following are geometric series?

- \frac{1}{2}, \frac{1}{2}, - \frac{3}{2} ...

3, 6, 10...

4, 8, 16...

4, 8, 12...

Question 2: Which of the following are geometric series?

9, - 3, 1...

\frac{1}{2}, \frac{1}{4}, - \frac{1}{9}

2, - 4, - 9...

1.5, 1, 0.5...

Question 3: Find a common ratio in the following geometric series:

5, 15, 45...

r = \frac{1}{3}

r = - 3

r = 5

r = 3

Question 4: Find the

14

th term in the following geometric series:

12, 6, 3...

a_{14} \approx 0.0172

a_{14} \approx 0.00146

a_{14} \approx 0.0031

a_{14} \approx 0.15

Question 5: Find the sum of the first

5

terms in the following series:

3 \frac{1}{2}, 7, 14, ...

S_{5} = 108.5

S_{5} = 98.5

S_{5} = 102.5

S_{5} = 98

Question 6: Find the sum of first

14

terms in the following series:

1, \frac{1}{4}, \frac{1}{16}, ...

S_{6} \approx 1.5

S_{6} \approx 1.66

S_{6} \approx 1.29

S_{6} \approx 1.33

Question 7: Find the sum to infinity of the following series:

5_{,} \frac{5}{3}, \frac{5}{9}, ...

S_{\infty} = 10

S_{\infty} = 8 \frac{2}{3}

S_{\infty} = 5

S_{\infty} = 7 \frac{1}{2}

Question 8: Find the sum to infinity of the following series:

7, - \frac{14}{5}, \frac{28}{25}, ...

S_{\infty} = 5

S_{\infty} = 6 \frac{7}{8}

S_{\infty} = 4 \frac{1}{2}

S_{\infty} = 5 \frac{9}{10}

Question 9: Find the range of values where the following series has a sum to infinity.

1 - \frac{2 x}{3} + \frac{4 x^{2}}{3} - \frac{8 x^{3}}{27} + ...

- \frac{1}{2} < x < \frac{1}{2}

- 1 < x < 1

- \frac{3}{2} < x < \frac{3}{2}

- \frac{2}{3} < x < \frac{2}{3}

Question 10: What is the least number of terms in the geometric series

1, 3, 9, ...

, if the sum exceeds

1000

n = 7

n = 8

n = 6

n = 9

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