Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20,
the 20th term of the sequence.
149)
22, 13 , 4, –5, . . .
149)
A)
an=9n – 31; a20 =149
B)
an=9n – 22; a20 =158
C)
an= – 9n + 31; a20 = – 149
D)
an= – 9n + 22; a20 = – 158
Solve the problem.
150)
To train for a race, Will begins by jogging 13 minutes one day per week. He increases his jogging
time by 5 minutes each week. Write the general term of this arithmetic sequence, and find how
many weeks it takes for him to reach a jogging time of one hour.
150)
A)
an=5n +13; 11 weeks
B)
an=5n +13; 10 weeks
C)
an=5n +8; 10 weeks
D)
an=5n +8; 11 weeks
Find the probability.
151)
A card is drawn from a well–shuffled deck of 52 cards. What is the probability of getting a red 5?
151)
A)
1
2
B)
1
4
C)
1
52
D)
1
26
Write the first four terms of the geometric sequence with the given first term, a1, and common ratio, r.
152)
a1=1; r =1
5
152)
A)
1, 5, 25, 125, . . .
B)
1
5, 1
25 , 1
125, 1
625, . . .
C)
1, 1
5, 1
25 , 1
125, . . .
D)
1, 6
5, 7
5, 8
5, . . .
Use the formula for the sum of the first n terms of a geometric sequence to solve.
153)
Find the sum of the first 13 terms of the geometric sequence: 7, –21, 63, –189, 567, . . . .
153)
A)
2,790,061
B)
2,790,074
C)
2,790,065
D)
2,790,067
Use the Binomial Theorem to expand the binomial and express the result in simplified form.
154)
(2x – 1)5
154)
A)
32x5– 16x4+ 8x3– 4x2+ 2x – 1
B)
(4x2– 4x + 1)5
C)
32x5+ 10x4– 40x3– 40x2+ 10x – 1
D)
32x5– 80x4+ 80x3– 40x2+ 10x – 1
Find the probability.
155)
Give the probability that the roll of a die will show a number less than 7.
155)
A)
1
6
B)
7
6
C)
1
Find the indicated sum.
156)
4
k = 2
k(k + 2)
156)
A)
32
B)
47
C)
24
D)
50
Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence.
157)
4
i = 1
2
5
i + 1
157)
A)
4124
3125
B)
406
625
C)
812
3125
D)
816
3125
D)
Find the indicated sum.
158)
4
i = 1
1
6i
158)
A)
25
72
B)
1
24
C)
11
36
D)
5
24
Solve the problem.
159)
As part of her retirement savings plan, Patricia deposited $400 in a bank account during her first
year in the workforce. During each subsequent year, she deposited $45 more than the previous
year. Find how much she deposited during her twentieth year in the workforce. Find the total
amount deposited in the twenty years.
159)
A)
$1300; $17,000
B)
$1255; $16,550
C)
$1255; $33,100
D)
$1300; $34,000
Evaluate the expression.
160)
10C6
8C4
–32!
30!
160)
A)
–1053
B)
–29
C)
989
D)
–989
Write the first four terms of the sequence whose general term is given.
161)
an=(–1)n + 1(n +4)
161)
A)
–5, 6, –7, 8
B)
5, –6, 7, –8
C)
5, –12, 21, –32
D)
–6, 7, –8, 9
43
162)
an=n4
(n + 1)!
162)
A)
1
2, 8
3, 27
4, 64
5
B)
1
2, 8
3, 27
8, 32
15
C)
2, 4
3, 1, 4
5
D)
2, 4
3, 1
2, 2
15
Solve the problem.
163)
On a gambling trip to Las Vegas, Anthony tripled his bet each time he won. If his first winning bet
was $2 and he won six consecutive bets, find how much he won on the sixth bet. Find the total
amount he won on these six bets.
163)
A)
$1458; $2186
B)
$486; $728
C)
$1458; $728
D)
$162; $242
Find the probability.
164)
What is the probability that a card drawn from a deck of 52 cards is not red?
164)
A)
3
4
B)
2
C)
1
2
D)
25
52
Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence.
165)
5
i = 1
1
3·2i
165)
A)
77
3
B)
62
3
C)
56
3
D)
53
3
A class is collecting data on eye color and gender. They organize the data they collected into a table. Numbers in the table
represent the number of students from the class that belong to each of the categories. Use the data to solve the problem.
Express probabilities as simplified fractions.
166)
Find the probability that a randomly selected student does not have blue eyes.
Brown Blue Green
Male 26 16 8
Female 20 14 16
166)
A)
9
25
B)
3
10
C)
7
10
D)
17
50
Find the probability.
167)
A bag contains 7 red marbles, 5 blue marbles, and 4 green marbles. What is the probability of
choosing a blue marble when one marble is drawn?
167)
A)
5
16
B)
1
4
C)
7
16
D)
5
12
Use the formula for the sum of the first n terms of a geometric sequence to solve.
168)
Find the sum of the first six terms of the geometric sequence: 3, 12, 48, . . . .
168)
A)
1365
B)
4095
C)
63
D)
971
Find the indicated sum.
169)
5
i = 1
(i + 3)
169)
A)
12
B)
30
C)
22
D)
8
45
Write the first five terms of the arithmetic sequence with the given first term, a1, and common difference, d.
170)
a1= – 0.4, d =0.9
170)
A)
–1.3, –2.2, –3.1, –4, –4.9
B)
–0.4, 0.5, 1.4, 2.3, 3.2
C)
–0.4, –1.3, –2.2, –3.1, –4
D)
0.5, 1.4, 2.3, 3.2, 4.1
Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
171)
1
3+1
2+3
5+ . . . +7
8
171)
A)
14
i =2
i
i + 1
B)
14
i = 0
i
i +2
C)
n
i = 1
i
i +2
D)
14
i = 1
i
i +2
Solve the problem.
172)
When students at State University held a food drive for the needy, 2916 cans of food were collected
on the first day of the drive, 972 the second day, 324 the third day, and so on. Find the total number
of cans collected the first five days.
172)
A)
7380 cans
B)
4368 cans
C)
4356 cans
D)
4320 cans
Find the probability.
173)
Each of ten tickets is marked with a different number from 1 to 10 and put in a box. If you draw a
ticket from the box, what is the probability that you will draw 4, 7, or 6?
173)
A)
1
4
B)
1
7
C)
3
10
D)
1
10
Find the sum of the infinite geometric series, if it exists.
174)
2+2
5+2
25 +2
125 + . . .
174)
A)
2
5
B)
does not exist
C)
12
5
D)
5
2
Write the first four terms of the geometric sequence with the given first term, a1, and common ratio, r.
175)
a1= – 6; r =5
175)
A)
–6, –1, 4, 9, . . .
B)
–6, –30, –150, –750, . . .
C)
–6, 30, –150, 750, . . .
D)
–30, –150, –750, –3750, . . .
Provide an appropriate response.
176)
Write the first five terms of the sequence whose general term is an=(–1)n + 1
n2.
176)
A)
1, –1
4, 1
9, –1
16 , 1
25
B)
1, 1
4, 1
9, 1
16 , 1
25
C)
1
2, –1
4, 1
9, –1
16 , 1
25
D)
–1, 1
4, –1
9, 1
16 , –1
25
Solve the problem.
177)
A restaurant offers a choice of 4 salads, 9 main courses, and 4 desserts. How many possible
3–course meals are there?
177)
A)
17 possible meals
B)
288 possible meals
C)
144 possible meals
D)
36 possible meals
Use the Binomial Theorem to expand the binomial and express the result in simplified form.
178)
(x + 2y)5
178)
A)
x5+ 10x4y + 80x3y2+ 160x2y3+ 80xy4+ 2y5
B)
x5+ 10x4y + 80x3y2+ 160x2y3+ 80xy4+ 32y5
C)
x5+ 10x4y + 40x3y2+ 80x2y3+ 80xy4+ 32
D)
x5+ 10x4y + 40x3y2+ 80x2y3+ 80xy4+ 32y5
179)
(4x – 5y)3
179)
A)
16x3y – 40x2y2+ 25xy3
B)
64x3– 80x2y + 100xy2– 125y3
C)
64x3– 240x2y + 300xy2– 125y3
D)
16x3y – 20x2y2+ 25xy3
Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
180)
32+63+94+ . . . +249
180)
A)
8
i = 1
2(i – 1)i + 1
B)
8
i = 1
3i2i – 1
C)
8
i = 1
(3i)i
D)
8
i = 1
(3i)i + 1
Find the probability.
181)
What is the probability that a card drawn from a deck of 52 cards is not a spade?
181)
A)
1
4
B)
2
5
C)
4
13
D)
3
4
Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of
summation.
182)
5+6+7+8+ . . . +21
182)
A)
22
k =6
(k – 1)
B)
21
k =5
(k – 1)
C)
16
k = 1
(k – 1)
D)
20
k =4
(k – 1)
Provide an appropriate response.
183)
Find the sum of the infinite geometric series: 4+4
4+4
42+4
43+ . . . .
183)
A)
5
B)
16
3
C)
does not exist
D)
1
Evaluate the expression.
184)
4C2·4C1
16C13
184)
A)
3
70
B)
9
14
C)
3
35
D)
1
70
Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20,
the 20th term of the sequence.
185)
a1= – 1
5, d = – 2
5
185)
A)
an= – 1
5n –1
5; a20 = – 21
5
B)
an= – 2
5n –1
5; a20 = – 41
5
C)
an= – 2
5n +1
5; a20 = – 39
5
D)
an= – 1
5n –2
5; a20 = – 22
5
Solve the problem.
186)
How many 2–letter codes can be formed using the letters A, B, C, D, E, and F? No letter can be used
more than once.
186)
A)
30
B)
15
C)
360
D)
720
Write a formula for the general term (the nth term) of the geometric sequence.
187)
4, 1, 1
4, 1
16 , 1
64 , . . .
187)
A)
an=41
16
n – 1
B)
an=41
4
n – 1
C)
an=41
4
n
D)
an=41
4
n + 1
Solve the problem. Round to the nearest hundredth of a percent if needed.
188)
A traffic engineer is counting the number of vehicles by type that turn into a residential area. The
table below shows the results of the counts during a four–hour period. What is the probability that
the next vehicle passing is an SUV?
Type of vehicle Number
Car 272
SUV 411
Van 61
Small truck 285
Large truck 202
Dump truck 25
Other 67
188)
A)
31.07%
B)
32.72%
C)
31.66%
D)
20.56%
Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence
with the given first term, a1, and common difference, d.
189)
Find a 28 when a1= – 1, d = – 3 .
189)
A)
–85
B)
80
C)
–82
D)
83
Find the probability.
190)
An urn contains balls numbered 1 through 10. A ball is chosen, returned to the urn, and a second
ball is chosen. What is the probability that the first and second balls will be a 7?
190)
A)
7
20
B)
1
100
C)
1
5
D)
7
10
Find the indicated sum.
191)
12
i =9
1
i – 4
191)
A)
–3280
6561
B)
323
495
C)
26
D)
533
840
Use the formula for nPr to evaluate the expression.
192)
7P4
192)
A)
5040
B)
840
C)
210
D)
1260
Write the first four terms of the sequence whose general term is given.
193)
an= – 1
3
n
193)
A)
1
3, –1
6, 1
9, –1
12
B)
–1
3, –1
9, –1
27 , –1
81
C)
–1
3, 1
9, –1
27 , 1
81
D)
–1
3, 1
6, –1
9, –1
12
Provide an appropriate response.
194)
Use the Binomial Theorem to expand and simplify: (x2+ 8)5.
194)
A)
x5+ 40x4+ 640x3+ 5120x2+ 20,480x + 32,768
B)
x10 + 40x8+ 1280x6+ 10,240x4+ 20,480x2+ 32,768
C)
x10 + 40x8+ 640x6+ 5120x4+ 20,480x2+ 32,768
D)
x7+ 40x6+ 640x5+ 5120x4+ 20,480x3+ 32,768
Find the term indicated in the expansion.
195)
(x – 3y)12; 5th term
195)
A)
–13,365x4y8
B)
40,095x8y4
C)
40,095x4y8
D)
–13,365x8y5
Write the first four terms of the sequence whose general term is given.
196)
an=7n
196)
A)
0, 7, 14, 21
B)
8, 9, 10, 11
C)
6, 5, 4, 3
D)
7, 14, 21, 28
Find the probability.
197)
Give the probability that the roll of a die will show 5 or 4.
197)
A)
1
3
B)
5
6
C)
2
D)
2
3
Express the repeating decimal as a fraction in lowest terms.
198)
0.3=3
10 +3
100 +3
1000 +3
10,000 + . . .
198)
A)
3
10
B)
3
100
C)
10
3
D)
1
3
Solve the problem.
199)
A club elects a president, vice–president, and secretary–treasurer. How many sets of officers are
possible if there are 11 members and any member can be elected to each position? No person can
hold more than one office.
199)
A)
330
B)
7920
C)
990
D)
495
Use the partial sum formula to find the partial sum of the given arithmetic sequence.
200)
Find the sum of the first eight terms of the arithmetic sequence: –10, –13, –16, . . . .
200)
A)
– 164
B)
164
C)
–104
D)
–39
Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20,
the 20th term of the sequence.
201)
26, 22 , 18, 14, . . .
201)
A)
an=4n – 26; a20 =54
B)
an=26 – 4n; a20 = – 54
C)
an=4n – 30; a20 =50
D)
an=30 – 4n; a20 = – 50
Use the Binomial Theorem to expand the binomial and express the result in simplified form.
202)
(3x – 2)4
202)
A)
–162x4+ 432 x3+ 216x2+ 192x + 16
B)
81x4–16x4
C)
81x3– 216x2+ 216x – 96
D)
81x4– 216x3+ 216x2– 96x + 16
Solve the problem. Round to the nearest hundredth of a percent if needed.
203)
A survey of 1001 adult investors asked how often they tracked their portfolio. The table shows the
investor responses. What is the probability that an adult investor tracks his or her portfolio daily?
How frequently? Response
Daily 233
Weekly 282
Monthly 275
Couple times a year 150
Don’t track 61
203)
A)
28.17%
B)
24.79%
C)
27.47%
D)
23.28%
Write the first four terms of the sequence whose general term is given.
204)
an=3(n + 1 )!
n!
204)
A)
4, 5, 6, 7
B)
6, 9
2, 2, 5
8
C)
6, 9
2, 4, 15
4
D)
6, 9, 12, 15
54
Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
205)
27
i = 1
(5i +2)
205)
A)
1944
B)
2025
C)
2119.5
D)
1876.5
Use the Binomial Theorem to expand the binomial and express the result in simplified form.
206)
(3x + 5)3
206)
A)
9x2+ 30x + 25
B)
27x3+ 135x2+ 135x + 125
C)
9x6+ 15x3+ 15,625
D)
27x3+ 135x2+ 225x + 125
Express the repeating decimal as a fraction in lowest terms.
207)
0.62 =62
100 +62
10,000 +62
1,000,000 + . . .
207)
A)
31
500
B)
31
50
C)
62
99
D)
6200
99
Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
208)
33
i = 1
(–6i – 4)
208)
A)
–3498
B)
–3217.5
C)
–3399
D)
–3333
Solve the problem.
209)
Lonnie deposits $125 each month into an account paying annual interest of 5% compounded
monthly. How much will his account have in it at the end of 10 years? (Round to the nearest dollar.)
209)
A)
$19,539
B)
$19,410
C)
$1572
D)
$19,256
Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20,
the 20th term of the sequence.
210)
3, 12 , 21 , 30 , 39 , . . .
210)
A)
an=9n – 6; a20 =174
B)
an=9n –2; a20 =178
C)
an=6n –9; a20 =111
D)
an=6n –2; a20 =118
Provide an appropriate response.
211)
Use the Binomial Theorem to write the first three terms in the expansion and simplify: (x + 2y2)9.
211)
A)
x9+ 20 x8y2+ 144 x7y4
B)
x9+ 18 x8y2+ 288 x7y4
C)
x9+ 18 x8y2+ 144 x7y4
D)
x9+ 20 x8y2+ 288 x7y4
Find the probability.
212)
What is the probability that the arrow will land on 3 or 1?
212)
A)
2
5
B)
1
C)
3
D)
1
3
D)
Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
213)
a + 1 +a + 2
2+ . . . +a +4
4
213)
A)
4
i = 0
a + i
i
B)
n
i = 0
a + i
i
C)
4
i = 1
a + i
i
D)
n
i = 1
a + i
i
Solve the problem.
214)
How many six–digit codes using the numbers 0 through 9 can be formed if the first three digits are
204?
214)
A)
1000 codes can be formed
B)
210 codes can be formed
C)
729 codes can be formed
D)
1,000,000 codes can be formed
Use the formula for the sum of the first n terms of a geometric sequence to solve.
215)
Find the sum of the first five terms of the geometric sequence: 1
3, 4
3, 16
3, . . . .
215)
A)
68
3
B)
341
3
C)
340
3
D)
341
15
Write the first four terms of the sequence whose general term is given.
216)
an=(–4)n
216)
A)
–4, 16, –64, 256
B)
4, –16, –64, –256
C)
–4, –16, –64, –256
D)
4, –16, 64, –256
217)
an=2(n +1)!
217)
A)
4, 12, 48, 240
B)
2, 4, 12, 48
C)
2, 8, 36, 192
D)
4, 24, 144, 960
Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of
summation.
218)
a + ar + ar2+ . . . + ar13
218)
A)
14
k = 1
ark
B)
13
k = 1
ark
C)
13
k = 0
(ar)k
D)
13
k = 0
ark
Use the Binomial Theorem to expand the binomial and express the result in simplified form.
219)
(x + 3y)3
219)
A)
x3+ 3x2y + 6xy + 9xy2+ 18y2+ 27y3
B)
x3+ 27y3
C)
3x +9y
D)
x3+ 9x2y + 27xy2+ 27y3
Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
220)
45
i = 1
(5i – 5)
220)
A)
4837.5
B)
5332.5
C)
5175
D)
4950
Use the formula for the sum of the first n terms of a geometric sequence.
221)
Find
17
i = 1
(–2)i.
221)
A)
43,690
B)
–87,382
C)
–43,690
D)
–174,762
Solve the problem.
222)
In how many ways can 6 players be assigned to 6 positions on a baseball team, assuming that any
player can play any position?
222)
A)
720 ways
B)
30 ways
C)
1440 ways
D)
360 ways
Find the probability.
223)
A card is drawn from a well–shuffled deck of 52 cards. What is the probability of drawing an ace or
a 6?
223)
A)
13
2
B)
7
26
C)
7
D)
2
13
Evaluate the expression.
224)
5P3
3! –5C3
224)
A)
120
B)
2
C)
0
D)
6
Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence
with the given first term, a1, and common ratio, r.
225)
Find a8 when a1=30,000, r = – 0.1.
225)
A)
–0.003
B)
0.003
C)
0.0003
D)
–0.03
Find the common difference for the arithmetic sequence.
226)
8, 12, 16, 20, . . .
226)
A)
–4
B)
4
C)
–12
D)
12
Solve the problem.
227)
A group of students consists of 18 male freshmen, 7 female freshmen, 20 male sophomores, and 5
female sophomores. If one person is randomly selected from the group, find the probability of
selecting a sophomore or a female.
227)
A)
16
25
B)
3
5
C)
37
50
D)
17
50
Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence
with the given first term, a1, and common ratio, r.
228)
Find a8 when a1=5,000,000, r = 0.1.
228)
A)
5
B)
0.005
C)
0.5
D)
0.05
Use the formula for the sum of the first n terms of an arithmetic sequence.
229)
Find the sum of the first 30 terms of the arithmetic sequence: –5, –14, –23, –32, . . .
229)
A)
–4055
B)
–4065
C)
–4200
D)
–275