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 –5, –1.666666666667,
–0.555555555556, –0.185185185185, . . . is
A |  | C | –3 | B | 3 | D |  |
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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 | 2 | C |  | B | 3 | D |  |
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3.
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The eighth term in the sequence 59 049, 19 683, 6561, 2187, … is
A | 27 | C | 9 | B | 3 | D |  |
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4.
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How many terms are in the sequence 6, 42, 294, 2058, 14406, …, 1 694 851
494?
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5.
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The sum of the geometric series 7 + 0.7 + 0.07 +  + 0.000007 is
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6.
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The 8th term of the geometric series 256 + 128 + 64 +  is
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7.
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What is the value of S10 for the series 7 – 35 + 175
– 875 +  ? A | –11 393 229 | C | –13 671 874 | B | –11 393 228 | D | 2 278 646 |
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8.
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Determine the sum of the infinite geometric series 27 +  +  +
 +...
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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 33 + (  ) + (  ) +
(  ) +  ? A | The series is convergent and has a sum of  . | B | The series is
convergent and has no sum. | C | The series is divergent 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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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, r = 2
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3.
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4.
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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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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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For a geometric series,  . What are the first three terms of the
series if the first term is 3?
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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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