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 8, 1, 0.125, 0.015625, . . . is
A |  | C | 8 | B | –8 | D |  |
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2.
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The population of a community was 82 000 at the beginning of 2000. Assuming a
rate of growth of 1.6% per year since 2000, what will the population be at the beginning of
2025?
A | 123 894 | C | 121 943 | B | 2 082 800 | D | 120 023 |
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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 2, 8, 32, 128, 512, …, 2 097
152?
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5.
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The sum of a geometric series where  , r = 2, and n = 3 is
approximately
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6.
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The sum of the geometric series 14 + 70 + 350 +  + 43 750 is A | 8747 | C | 54 688 | B | 10 938 | D | 54 684 |
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7.
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The 6th term of the geometric series 256 + 128 + 64 +  is
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8.
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Determine the sum of the infinite geometric series 11 +  +  +
 +...
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9.
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What is the sum of the infinite geometric series 15 +  +  +
 +  ?
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10.
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Which of the following best describes the series –50 + (  ) + (  ) +
(  ) +  ? A | The series is convergent and has a sum of  . | B | The series is
divergent and has a sum of  . | C | The series is divergent and has no
sum. | D | The series is convergent and has no sum. |
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Short Answer
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For each geometric sequence, determine
a) an explicit formula for
the general term
b) 
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1.
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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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For each sequence, determine i) an explicit formula for the nth
term, using function notation ii) f(11) a)  b) 5, 13, 25,
41, 61, … c) 
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2.
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In a lottery, the first ticket drawn wins a prize of $25. Each ticket after that
receives a prize that is twice the value of the preceding prize.
a) Write a function to
model the total amount of prize money given away.
b) How many prizes are given out if the
total amount of prize money is approximately $2 million?
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3.
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One side of an equilateral triangle is 10 cm. The midpoints of its sides are
joined to form an inscribed equilateral triangle, and this process is continued, as shown in the
diagram.  What is the sum of the perimeters of the triangles if
this process is continued without end?
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