Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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The common ratio for the geometric sequence –9, –0.9, –0.09,
–0.009, . . . is
A | –10 | C |  | B | 10 | D |  |
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2.
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The population of a community was 93 000 at the beginning of 2000. Assuming a
rate of growth of 2.6% per year since 2000, what will the population be at the beginning of
2031?
A | 211 446 | C | 2 957 958 | B | 200 865 | D | 206 087 |
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3.
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The eighth term in the sequence 196 608, 49 152, 12 288, 3072, … is
A |  | C | 4 | B | 12 | D | 3 |
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4.
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The 9th term in the sequence  , 1,  ,  , . . .
is
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5.
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The sum of a geometric series where  , r = 5, and n = 3 is
approximately
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6.
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The sum of the geometric series 9 + 36 + 144 +  + 36 864 is A | 12 288 | C | 49 152 | B | 49 149 | D | 9214 |
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7.
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The 7th term of the geometric series 1024 + 512 + 256 +  is
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8.
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Determine the sum of the infinite geometric series 17 +  +  +
 +...
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9.
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What is the sum of the infinite geometric series 7 +  +  +
 +  ?
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10.
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Which of the following best describes the series –50 + (  ) + (  ) +
(  ) +  ? A | The series is divergent and has a sum of  . | B | The series is
convergent and has no sum. | C | The series is convergent and has a sum of  . | D | The series is divergent and has no sum. |
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Short Answer
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Determine whether each sequence is geometric, arithmetic, or neither. Justify
your answer.
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1.
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5, –10, 20, –40, …
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2.
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0.0005, 0.005, 0.05, 0.5, …
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For each geometric sequence, determine
a) an explicit formula for
the general term
b) 
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3.
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4.
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A bouncy ball bounces to  its height when it is dropped on a hard
surface. Suppose the ball is dropped from 20 m. a) What height will the ball bounce back up
to after the sixth bounce? b) What is the total distance the ball travels if it bounces
indefinitely?
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Problem
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1.
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A ball is kicked 26 m into the air. The ball falls, rebounds to half of its
original height, and then falls to the ground again. This pattern of rebounding to half of the height
from the previous bounce continues. a) Use this information to determine 
and r for the geometric sequence that represents this situation. b) Write an
explicit formula for the general term. c) Write a formula for the total distance travelled
after n bounces. d) If 7 bounces occur, i) how high will the seventh
bounce be? ii) what total distance will the ball have travelled?
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2.
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The first prize in a lottery is $250 000. Each winner chosen after the first is
paid 20% as much as the winner before them.
a) Determine t1 and r
for the geometric sequence that represents this situation.
b) Determine an explicit
formula for the general term.
c) Determine a formula for the sum of n terms of the
geometric sequence.
d) If 5 winning numbers are chosen,
i) how much will the last
person chosen be paid?
ii) how much will have been paid out in the lottery?
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3.
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Write each repeating decimal number as an equivalent fraction in lowest
terms. a) 0.5555... b) 
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