Use the Binomial Theorem to expand the binomial and express the result in simplified form.
74)
(x – 8)5
74)
A)
x5– 40x4+ 640x3– 5120x2+ 20,480x – 8
B)
x5– 40x4+ 640x3– 5120x2+ 20,480x – 32,768
C)
x5– 40x4+ 1280x3– 10,240x2+ 20,480x – 32,768
D)
x5– 40x4+ 1280x3– 10,240x2+ 20,480x – 8
Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of
summation.
75)
13+23+33+ . . . +83
75)
A)
8
k = 0
k3
B)
i
k =1
k3
C)
8
k =2
(k – 1)3
D)
8
k =1
k3
76)
76)
5+6+7+8+ . . . +34
A)
29
k = 1
(k – 1)
B)
34
k =5
(k – 1)
C)
33
k =4
(k – 1)
D)
35
k =6
(k – 1)
Find the common difference for the arithmetic sequence.
77)
77)
2, –1, –4, –7, . . .
A)
9
B)
–9
C)
–6
D)
–3
Use the formula for the sum of the first n terms of a geometric sequence to solve.
78)
Find the sum of the first 8 terms of the geometric sequence: 1
8, 3
8, 9
8, 27
8, 81
8, . . . .
78)
A)
3287
8
B)
1637
4
C)
410
D)
1639
4
Provide an appropriate response.
79)
Express 0.68 in fractional notation.
79)
A)
17
250
B)
6800
99
C)
17
25
D)
68
99
Solve the problem.
80)
80)
To save for retirement, you decide to deposit $2250 into an IRA at the end of each year for the
next 30 years. If the interest rate is 5% per year compounded annually, find the value of the IRA
after 30 years. (Round to the nearest dollar.)
A)
$1,179,752
B)
$140,226
C)
$7474
D)
$149,487
Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of
summation.
81)
3+7
2+4+9
2+ . . . +15
2
81)
A)
15
k = 1
k
2
B)
10
k =6
k
2
C)
15
k =6
k
2
D)
15
k = 2
k
2
22
Write the first four terms of the sequence whose general term is given.
82)
an=n
n2+ 2
82)
A)
1
3, 3
11 , 2
9, 5
27
B)
1
2, 1
3, 3
8, 2
5
C)
1
3, 1
3, 3
8, 2
5
D)
1
3, 1
3, 3
11 , 2
9
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.
83)
83)
Find a8 when a1= – 5, r = – 3.
A)
–32,805
B)
10,939
C)
–26
D)
10,935
Evaluate the given binomial coefficient.
84)
6
2
84)
A)
1
B)
6
C)
15
D)
0
Write the first four terms of the sequence whose general term is given.
85)
an=(n + 1)!
n4
85)
A)
2, 3
8, 8
27 , 15
32
B)
1
2, 3
4, 1, 5
4
C)
1
2, 3
4, 2, 15
2
D)
2, 3
8, 4
27 , 5
64
23
Find the sum of the infinite geometric series, if it exists.
86)
1
6–2
3+8
3– . . .
86)
A)
does not exist
B)
1
30
C)
–8192
3
D)
32,768
3
Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
87)
1
3+1
2+3
5+ . . . +13
15
87)
A)
13
i = 0
i
i +2
B)
13
i = 1
i
i +2
C)
n
i = 1
i
i +2
D)
13
i =2
i
i + 1
Write the first three terms in the binomial expansion, expressing the result in simplified form.
88)
(x + 2)14
88)
A)
x14 + 26x13 + 364x12
B)
x14 + 26x13 + 728x12
C)
x14 + 28x13 + 728x12
D)
x14 + 28x13 + 364x12
Use the partial sum formula to find the partial sum of the given arithmetic sequence.
89)
89)
Find the sum of the first four terms of the arithmetic sequence: –3, –15, –27, . . . .
A)
–45
B)
– 84
C)
84
D)
–60
Provide an appropriate response.
90)
Find the indicated sum:
5
i = 1
(i2+ 6) .
90)
A)
42
B)
85
C)
30
D)
68
Express the repeating decimal as a fraction in lowest terms.
91)
0.35 =35
100 +35
10,000 +35
1,000,000 + . . .
91)
A)
7
200
B)
35
99
C)
3500
99
D)
7
20
Find the common ratio for the geometric sequence.
92)
2, 6
5, 18
25 , 54
125 , . . .
92)
A)
2
3
B)
5
3
C)
3
5
D)
1
5
Write the first five terms of the arithmetic sequence with the given first term, a1, and common difference, d.
93)
93)
a1= – 1.7, d = – 1.5
A)
–0.2, 1.3, 2.8, 4.3, 5.8
B)
–1.7, –3.2, –4.7, –6.2, –7.7
C)
–3.2, –4.7, –6.2, –7.7, –9.2
D)
–1.7, –0.2, 1.3, 2.8, 4.3
94)
94)
a1=18; d = – 4
A)
22, 17, 12, 7, 2
B)
0, 18, 14, 10, 6
C)
18, 14, 10, 6, 2
D)
–18, –14, –10, –6, –2
Solve the problem.
95)
95)
The population of a town is increasing by 400 inhabitants each year. If its current population is
29,089 and this trend continues, what would its population be in 8 years?
A)
31,889 inhabitants
B)
232,600 inhabitants
C)
32,289 inhabitants
D)
465,200 inhabitants
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.
96)
a1= – 3
4, d =5
4
96)
A)
an= – 3
4n +5
4; a20 = – 55
4
B)
an=5
4n – 2; a20 =23
C)
an=5
4n –3
4; a20 =97
4
D)
an= – 3
4n + 2; a20 = – 13
Write the first four terms of the geometric sequence with the given first term, a1, and common ratio, r.
97)
97)
a1=9; r =2
A)
9, 11, 13, 15, . . .
B)
9, 18, 36, 72, . . .
C)
2, 18, 162, 1458, . . .
D)
18, 36, 72, 144, . . .
Provide an appropriate response.
98)
Write the first five terms of the sequence whose general term is an=(–2)n + 1
n2.
98)
A)
4, 2, 16
9, 2, 64
25
B)
4, – 2, 16
9, – 2, 64
25
C)
–2, 1, –8
9, 1, –32
25
D)
2, – 2, 16
9, – 2, 64
25
Evaluate the given binomial coefficient.
99)
5
1
99)
A)
5!
B)
1
C)
5
4
D)
5
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.
100)
100)
Find a8 when a1=5,000,000, r = 0.1.
A)
0.005
B)
5
C)
0.5
D)
0.05
Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
101)
25
i = 1
(2i – 7)
101)
A)
450
B)
675
C)
475
D)
587.5
Find the common ratio for the geometric sequence.
102)
4
3, 8
3, 16
3, 32
3, 64
3, . . .
102)
A)
6
B)
not geometric
C)
2
3
D)
2
Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
103)
52+103+154+ . . . +409
103)
A)
8
i = 1
2(i – 1)i + 1
B)
8
i = 1
(5i)i + 1
C)
8
i = 1
5i2i – 1
D)
8
i = 1
(5i)i
Find the indicated sum.
104)
4
i = 1
1
4i
104)
A)
25
48
B)
11
24
C)
5
16
D)
1
16
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.
105)
105)
Find a6 when a1=7, r = – 5.
A)
109,375
B)
21,875
C)
–21,875
D)
–3125
Use the formula for the sum of the first n terms of a geometric sequence.
106)
Find
17
i = 1
(–2)i.
106)
A)
–174,762
B)
–43,690
C)
43,690
D)
–87,382
Find the term indicated in the expansion.
107)
(3x + 4)5; 5th term
107)
A)
960x
B)
2880x2
C)
3840x
D)
5120
Write the first three terms in the binomial expansion, expressing the result in simplified form.
108)
(x2+ 2)9
108)
A)
x18 + 20x16 + 144x14
B)
x18 + 20x16 + 288x14
C)
x18 + 18x16 + 288x14
D)
x18 + 18x16 + 144x14
Write the first four terms of the sequence whose general term is given.
109)
109)
an=4n – 1
A)
3, 4, 5, 6
B)
–3, –7, –11, –15
C)
5, 9, 13, 17
D)
3, 7, 11, 15
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.
110)
110)
Find a11 when a1=20, d = – 6.
A)
–40
B)
–46
C)
80
D)
–60
Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
111)
48
i = 1
(4i +7)
111)
A)
4944
B)
5040
C)
5352
D)
5184
Write the first four terms of the sequence whose general term is given.
112)
an=4
n2
112)
A)
4, 4
4, 4
9, 4
16
B)
1, 1
4, 1
9, 1
16
C)
1, 2
4, 3
9, 4
16
D)
4
4, 4
9, 4
16 , 4
25
Find the sum of the infinite geometric series, if it exists.
113)
i = 1
21
2
i – 1
113)
A)
2
B)
1
C)
4
D)
does not exist
Solve the problem.
114)
114)
To train for a race, Will begins by jogging 11 minutes one day per week. He increases his jogging
time by 3 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.
A)
an=3n +8; 18 weeks
B)
an=3n +8; 17 weeks
C)
an=3n +11; 17 weeks
D)
an=3n +11; 18 weeks
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.
115)
Find a6 when a1=11,200, r = – 1
2.
115)
A)
–35
B)
–350
C)
–175
D)
350
116)
116)
Find a9 when a1= – 5, r =2.
A)
–1280
B)
–1276
C)
11
D)
–2560
Find the indicated sum.
117)
5
i = 3
(i2+ 8)
117)
A)
95
B)
48
C)
74
D)
36
31
Evaluate the given binomial coefficient.
118)
3
3
118)
A)
0
B)
1
C)
6
D)
2
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.
119)
Find a12 when a1=1000, r =1
3.
119)
A)
1000
1,594,323
B)
1000
531,441
C)
3011
3
D)
1000
177,147
Find the term indicated in the expansion.
120)
(x + 2y)10; 7th term
120)
A)
13,440x6y4
B)
13,440x4y6
C)
6720x4y7
D)
6720x6y4
Find the indicated sum.
121)
5
i = 1
(i – 1)!
(i + 2)!
121)
A)
43
20
B)
241
140
C)
5
21
D)
37
30
Write the first four terms of the sequence whose general term is given.
122)
an=(–1)n(n +4)
122)
A)
5, 6, 7, 8
B)
–5, –12, –21, –32
C)
–5, 6, –7, 8
D)
–5, –6, –7, –8
Solve the problem.
123)
123)
A person puts $27 into a bank account on January 1, $32 on February 1, $37 on March 1, and so
forth. How much has the person put into the bank account by December 30?
A)
$1308
B)
$654
C)
$492
D)
$684
Express the repeating decimal as a fraction in lowest terms.
124)
0.321
124)
A)
13
37
B)
321
1000
C)
117
1000
D)
107
333
Use the Binomial Theorem to expand the binomial and express the result in simplified form.
125)
(x + 2y)3
125)
A)
x3+ 6x2y + 12xy2+ 8y3
B)
x3+ 2x2y + 4xy + 4xy2+ 8y2+ 8y3
C)
x3+ 8y3
D)
3x +6y
33
Solve the problem.
126)
126)
A job pays a salary of 31,000 the first year. During the next 9 years, the salary increases by 4%
each year. What is the salary for the 10th year? What is the total salary over the 10–year period?
Round to the nearest cent.
A)
$45,887.57; $418,076.89
B)
$45,887.57; $328,091.65
C)
$44,122.67; $328,066.65
D)
$44,122.67; $372,189.32
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.
127)
127)
Find a8 when a1=5, r = – 3.
A)
–10,931
B)
–16
C)
–10,935
D)
32,805
Write the first four terms of the geometric sequence with the given first term, a1, and common ratio, r.
128)
a1=7; r =1
4
128)
A)
7, 7
4, 7
16 , 7
64 , . . .
B)
7
4, 7
16 , 7
64 , 7
256 , . . .
C)
7, 29
4, 15
2, 31
4, . . .
D)
7, 28, 112, 448, . . .
129)
a1=1
5, r = – 6
129)
A)
1
5, –6
25 , –6
125 , –1296
625 , . . .
B)
1
5, –6
5, –36
5, –216
5, . . .
C)
1
5, –6
25 , 6
125 , –216
625 , . . .
D)
1
5, –6
5, 36
5, –216
5, . . .
Write a formula for the general term (the nth term) of the geometric sequence.
130)
130)
2, –6, 18, –54, 162, . . .
A)
an=2(–3)n
B)
an=a1– 3n
C)
an=2(–3n)
D)
an=2(–3)n – 1
Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
131)
65
i = 1
–3i
131)
A)
–6534
B)
–6336
C)
–6432
D)
–6435
Solve the problem.
132)
132)
A pendulum bob swings through an arc 50 inches long on its first swing. Each swing thereafter, it
swings only 60% as far as on the previous swing. How far will it swing altogether before coming
to a complete stop?
A)
63 in.
B)
83 in.
C)
167 in.
D)
125 in.
Write the first four terms of the geometric sequence with the given first term, a1, and common ratio, r.
133)
133)
a1=6, r = – 10
A)
6, –60, 600, –6000, . . .
B)
6, –60, –360, –2160, . . .
C)
6, –60, 360, –2160, . . .
D)
6, –60, –600, –6000, . . .
Use the Binomial Theorem to expand the binomial and express the result in simplified form.
134)
(x + 2)3
134)
A)
x3+ 8
B)
x3+ 2x2+ 4x + 8
C)
3x +6
D)
x3+ 6x2+ 12x + 8
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.
135)
135)
2, 6, 10 , 14 , 18 , . . .
A)
an= n +4; a20 =24
B)
an=4n + 2; a20 =82
C)
an=4n –2; a20 =78
D)
an=2n –4; a20 =36
Write a formula for the general term (the nth term) of the geometric sequence.
136)
1
6, –1
12 , 1
24 , –1
48 , . . .
136)
A)
an=1
6–1
2
n – 1
B)
an=1
6
n – 1
–1
4
C)
an=1
6–1
2(n – 1)
D)
an=1
2–1
6
n – 1
Provide an appropriate response.
137)
137)
Express the sum using summation notation. Use 1 as the lower limit of summation and i for the
index of summation.
3
4+4
5+5
6+ . . . +32
33
A)
30
i = 1
i
i +3
B)
30
i = 1
i +2
i +3
C)
30
i = 1
i
i +2
D)
31
i = 1
i +2
i +3
Use the partial sum formula to find the partial sum of the given arithmetic sequence.
138)
138)
Find the sum of the odd integers between 24 and 66.
A)
945
B)
900
C)
990
D)
1035
Use the Binomial Theorem to expand the binomial and express the result in simplified form.
139)
(x2+ 4y)4
139)
A)
x4+ 16x3y + 96x2y2+ 256xy3+ 256y4
B)
x8+ 4x6y + 96x4y2+ 128x2y3+ 256y4
C)
x8+ 16x6y + 96x4y2+ 256x2y3+ 256y4
D)
x8+ 16x6y + 96x4y2+ 16x2y3+ 256y4
Find the indicated sum.
140)
12
i =9
1
i + 3
140)
A)
543
1820
B)
54
C)
–323
660
D)
820
2187