Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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The population of a community was 38 000 at the beginning of 2000. Assuming a
rate of growth of 2.8% per year since 2000, what will the population be at the beginning of
2034?
A | 1 328 176 | C | 99 895 | B | 97 174 | D | 94 527 |
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2.
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In the formula for the general term of a geometric sequence  , the common
ratio is A |  | C | 9 | B | 2 | D |  |
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3.
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The 6th term in the sequence  , 1,  ,  , . . .
is
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4.
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How many terms are in the sequence 9, 72, 576, 4608, 36864, …, 618 475 290
624?
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5.
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The sum of the geometric series 13 + 39 + 117 +  + 9477 is
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6.
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The sum of the geometric series 8 + 4 + 2 +  + 0.25 is
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7.
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What is the value of S9 for the series 9 – 63 + 441
– 3087 +  ? A | 45 397 809 | C | 45 397 808 | B | –6 485 401 | D | 51 883 210 |
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8.
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What is the sum of the infinite geometric series 1 +  +  +
 +  ?
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9.
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Determine the sum of the infinite geometric series with t1 = 6
and r =  .
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10.
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Which of the following best describes the series –39 + (  ) + (  ) +
(  ) +  ? A | The series is divergent and has a sum of  . | B | The series is
divergent and has no sum. | C | The series is convergent and has a sum of  . | D | The series is convergent 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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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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2.
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3.
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If S1 = 0.7 and S2 = 2.1 in a geometric
series, determine the sum of the first 12 terms in the series. Be sure to show all of your
work.
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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 Registered Education Savings Plan (RESP) earns interest at a rate of 5% per
year, compounded annually. Jasmine’s parents invest $4000 in the account today.
a)
Determine an explicit formula to represent the value of the investment.
b) Use your formula
to write the first four terms of the sequence.
c) What will the investment be worth
in
i) 9 years?
ii) 16 years?
d) Approximately how long will it take for
the investment to double?
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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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