Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Which of the following numbers occurs in the sequence –12, –8,
–4, 0, 4, . . .?
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2.
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The common difference in the arithmetic sequence 2, –6, –14,
–22, . . . is
A | –8 | C | –16 | B |  | D | 8 |
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3.
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The common difference in the arithmetic sequence  ,  ,  ,
 ,  , . . . is A |  | C | 9 | B | 3 | D |  |
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4.
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In the formula for the general term of an arithmetic sequence
tn = –7 + (n – 1) ´
(–2.5), the common difference is
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5.
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Which of the given formulas for the general term of the sequence –9,
–1, 7, 15, 23, . . . is correct?
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6.
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The sum of the series (–5) + (–7) + (–9) +  + (–19)
is
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7.
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The sum of an arithmetic series where t1 = –2,
t3 = 7, and n = 15 is
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8.
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The sum of an arithmetic series where  ,  , and
n = 19 is
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9.
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For the arithmetic series (107) + (130) + (153) +  + (981), the values of
 , d, and n are A |  , d = 23, n = 39 | C |  =
–107, d = 23, n = 38 | B |  = 107, d = –23, n
= 39 | D |  =
–107, d = –23, n = 38 |
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10.
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On the first day of the month, Michael places 5¢ in a jar. The next day, he
places 7¢ in the jar. The third day, he places 9¢ in the jar, and so on for 24 days. What
amount will be in the jar at the end of this period of time?
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Short Answer
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For each arithmetic sequence, determine
a) the value of
t1 and d
b) an explicit formula for the general term
c)
t20
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1.
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–8, –5, –2, 1, …
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Determine whether each sequence is geometric, arithmetic, or neither. Justify
your answer.
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2.
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0.0005, 0.005, 0.05, 0.5, …
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For each arithmetic series, determine
a) an explicit formula for
the general term
b) a formula for the general sum
c) 
d) 
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3.
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 = 2, d = 3, n = 4
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Determine the sum of each arithmetic series.
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4.
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Problem
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1.
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At the end of the second week after opening, a new fitness club has 870 members.
At the end of the seventh week, there are 1110 members. Suppose the increase is
arithmetic.
a) How many members joined the club each week?
b) How many members
were there in the first week?
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2.
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In an arithmetic series, the sum of the first 5 terms is 70 and the sum of the
first 11 terms is 352. a) Determine the values of  and d. b)
What is the sum of the first i) 30 terms? ii) 50 terms? iii) 100
terms? c) Describe how you could use the formula for the sum of an arithmetic series to
find the total of terms 35 to 40. d) Use your method from part c) to determine the sum of
terms 35 to 40.
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