141)
4
i = 1
–1
3
i
141)
A)
20
81
B)
–16
81
C)
–20
81
D)
40
81
Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence.
142)
5
i = 1
2
3·4i
142)
A)
2728
3
B)
2785
3
C)
2707
3
D)
2692
3
Write the first four terms of the sequence whose general term is given.
143)
an=(–1)n + 1
n +8
143)
A)
–1
10 , 1
11 , –1
12 , 1
13
B)
1
9, –1
10 , 1
11 , –1
12
C)
–1
9, 1
10 , –1
11 , 1
12
D)
1
9, –1
20 , 1
33 , –1
48
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.
144)
144)
Find a90 when a1= – 14, d = – 5.
A)
–459
B)
431
C)
–464
D)
436
Solve the problem.
145)
145)
A deposit of $7000 is made in an account that earns 7.2% interest compounded quarterly. The
balance in the account after n quarters is given by the sequence
an=7000(1 +0.072
4)n, n = 1, 2, 3, …
Find the balance in the account after four years by computing a16
A)
$9312.42
B)
$4087.38
C)
$7517.77
D)
$5321.38
Find the indicated sum.
146)
4
k = 1
(–1)k(k + 1)
146)
A)
–14
B)
6
C)
14
D)
2
Write the first three terms in the binomial expansion, expressing the result in simplified form.
147)
(x + 4)20
147)
A)
x20 + 760x19 + 3040x18
B)
x20 + 80x19 – 3040x18
C)
x20 + 3040x19 + 3040x18
D)
x20 + 80x19 + 3040x18
Solve the problem.
148)
148)
Lonnie deposits $100 each month into an account paying annual interest of 7% compounded
monthly. How much will his account have in it at the end of 9 years? (Round to the nearest
dollar.)
A)
$1198
B)
$15,115
C)
$14,832
D)
$14,986
Find the common ratio for the geometric sequence.
149)
149)
16, 8, 4, 2, 1, . . .
A)
1
B)
0.5
C)
2
D)
–0.5
Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence.
150)
5
i = 1
4(–3)i
150)
A)
–732
B)
240
C)
69
D)
–2460
Solve the problem.
151)
151)
A pendulum bob swings through an arc 70 inches long on its first swing. Each swing thereafter, it
swings only 64% as far as on the previous swing. What is the length of the arc after 12 swings?
Round to two decimal places.
A)
0.21 in.
B)
0.33 in.
C)
492.80 in.
D)
0.52 in.
Evaluate the given binomial coefficient.
152)
80
78
152)
A)
246,480
B)
1580
39
C)
3160
D)
40
39
Find the term indicated in the expansion.
153)
(2x – 3y)11; 9th term
153)
A)
8,660,520x3y8
B)
–2,886,840x8y3
C)
–2,886,840x3y9
D)
4,330,260x8y3
Use the formula for the sum of the first n terms of an arithmetic sequence.
154)
154)
Find the sum of the first 60 terms of the arithmetic sequence: –16, –25, –34, –43, . . .
A)
–556
B)
–16,890
C)
–17,160
D)
–16,884
Solve the problem.
155)
155)
Jacie is considering a job that offers a monthly starting salary of $3000 and guarantees her a
monthly raise of $130 during her first year on the job. Find the general term of this arithmetic
sequence and her monthly salary at the end of her first year.
A)
an=2870 +130n; $4430
B)
an=3000 +130n; $4430
C)
an=3000 +130n; $4560
D)
an=2870 +130(n – 1); $4300
Find the common ratio for the geometric sequence.
156)
156)
9, 0.9, 0.09, 0.009, . . .
A)
0.01
B)
0.9
C)
0.1
D)
1
Write the first five terms of the arithmetic sequence with the given first term, a1, and common difference, d.
157)
157)
a1=1; d =2
A)
3, 5, 7, 9, 11
B)
1, 3, 5, 7, 9
C)
1, 2, 3, 4, 5
D)
0, 1, 3, 5, 7
Use the formula for the sum of the first n terms of a geometric sequence to solve.
158)
158)
Find the sum of the first 11 terms of the geometric sequence: –8, –24, –72, –216, –648, . . . .
A)
–708,584
B)
–708,582
C)
–708,604
D)
–708,547
Find the term indicated in the expansion.
159)
(5x + 3)5; 5th term
159)
A)
675x
B)
1215
C)
2025x
D)
3375x2
Solve the problem.
160)
160)
On a gambling trip to Las Vegas, Anthony doubled his bet each time he won. If his first winning
bet was $5 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.
A)
$160; $315
B)
$320; $635
C)
$80; $155
D)
$320; $315
Write the first four terms of the sequence whose general term is given.
161)
161)
an=5n
A)
6, 7, 8, 9
B)
5, 10, 15, 20
C)
4, 3, 2, 1
D)
0, 5, 10, 15
Find the sum of the infinite geometric series, if it exists.
162)
i = 1
5
3–1
3
i – 1
162)
A)
does not exist
B)
5
3
C)
5
4
D)
1
4
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.
163)
163)
Find a9 when a1=3, r =3.
A)
19,687
B)
27
C)
19,683
D)
59,049
Find the indicated sum.
164)
4
i = 1
2i
164)
A)
18
B)
30
C)
20
D)
14
Use the partial sum formula to find the partial sum of the given arithmetic sequence.
165)
165)
Find 1+3+5+7+ . . ., the sum of the first 55 positive odd integers.
A)
2970
B)
2966
C)
3029
D)
3025
Write the first five terms of the arithmetic sequence with the given first term, a1, and common difference, d.
166)
166)
a1= – 36; d =9
A)
–18, –27, –36, –45, –54
B)
–18, –9, 0, 9, 18
C)
0, –9, –18, –27, –36
D)
–36, –27, –18, –9, 0
Write a formula for the general term (the nth term) of the sequence. Then use the formula for an to find the twelfth
term of the sequence.
167)
25, 5, 1, 1
5, . . .
167)
A)
an=25 1
5
n + 1; a12 =1
48,828,125
B)
an=51
5
n – 1; a12 =1
9,765,625
C)
an=25 1
5
n; a12 =1
9,765,625
D)
an=25 1
5
n – 1; a12 =1
1,953,125
Provide an appropriate response.
168)
Evaluate: 11
9 .
168)
A)
55
B)
27
C)
110
D)
1
Find the sum of the infinite geometric series, if it exists.
169)
–12 – 3 –3
4–3
16 – . . .
169)
A)
– 16
B)
does not exist
C)
4
D)
–63
4
Find the common difference for the arithmetic sequence.
170)
170)
7, 9, 11, 13, . . .
A)
1.5
B)
2
C)
6
D)
7
Use the formula for the sum of the first n terms of a geometric sequence to solve.
171)
Find the sum of the first 11 terms of the geometric sequence: 1
6, –1
2, 3
2, –9
2, 27
2, . . . .
171)
A)
44,287
6
B)
44,281
6
C)
44,285
6
D)
22,147
3
Write the first four terms of the sequence whose general term is given.
172)
172)
an=4(2n – 3)
A)
–12, –4, 4, 12, 20
B)
–1, 1, 3, 5, 7
C)
–4, –8, –12, –16, –20
D)
–4, 4, 12, 20, 28
45
Write the first three terms in the binomial expansion, expressing the result in simplified form.
173)
(3x + 2y)7
173)
A)
7x7+ 6x6y + 5x5y2
B)
2187x7+ 10,206x6y + 20,412x5y2
C)
2187x7y + 10,206x6y2+ 20,412x5y3
D)
7x7y + 6x6y2+ 5x5y3
Write the first four terms of the sequence whose general term is given.
174)
an=(–4)n
174)
A)
–4, –16, –64, –256
B)
4, –16, 64, –256
C)
–4, 16, –64, 256
D)
4, –16, –64, –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.
175)
175)
27, 18 , 9, 0, . . .
A)
an=9n – 27; a20 =153
B)
an=27 – 9n; a20 = – 153
C)
an=9n – 36; a20 =144
D)
an=36 – 9n; a20 = – 144
Use the Binomial Theorem to expand the binomial and express the result in simplified form.
176)
(x – 3)4
176)
A)
x4– 12x3+ 54x2+ 12x + 81
B)
x4– 3x3+ 54x2– 54x + 81
C)
x4– 12x3– 54x2– 108x + 81
D)
x4– 12x3+ 54x2– 108x + 81
Find the common ratio for the geometric sequence.
177)
3
4, 3
16 , 3
64 , 3
256 , 3
1024 , . . .
177)
A)
1
4
B)
1
40
C)
4
D)
40
Find the sum of the infinite geometric series, if it exists.
178)
3– 1 +1
3–1
9+ . . .
178)
A)
– 1
B)
2
C)
does not exist
D)
9
4
Solve the problem.
179)
179)
Looking ahead to retirement, you sign up for automatic savings in a fixed–income 401K plan that
pays 5.5% per year compounded annually. You plan to invest $2000 at the end of each year for
the next 20 years. How much will your account have in it at the end of 20 years? (Round to the
nearest dollar.)
A)
$71,035
B)
$71,507
C)
$69,737
D)
$68,194
Use the Binomial Theorem to expand the binomial and express the result in simplified form.
180)
(3x – 2y)3
180)
A)
27x3– 54x2y + 36xy2– 8y3
B)
9x3y – 6x2y2+ 4xy3
C)
27x3– 18x2y + 12xy2– 8y3
D)
9x3y – 12x2y2+ 4xy3
Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
181)
a + 1 +a + 2
2+ . . . +a +5
5
181)
A)
n
i = 1
a + i
i
B)
5
i = 1
a + i
i
C)
5
i = 0
a + i
i
D)
n
i = 0
a + i
i
Write a formula for the general term (the nth term) of the geometric sequence.
182)
3, 1, 1
3, 1
9, 1
27 , . . .
182)
A)
an=31
3
n – 1
B)
an=31
3
n + 1
C)
an=31
3
n
D)
an=31
9
n – 1
Find the indicated sum.
183)
7
i =4
2i
183)
A)
14
B)
44
C)
30
D)
22
Find the common ratio for the geometric sequence.
184)
184)
4, –12, 36, –108, 324, . . .
A)
3
B)
–16
C)
–3
D)
–1
3
Write the first four terms of the sequence whose general term is given.
185)
an=
–2(n + 1 )!
n!
185)
A)
–4, – 3, –8
3, –5
2
B)
–1, 0, 1, 2
C)
–4, –6, –8, –10
D)
–4, – 3, –4
3, –5
12
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.
186)
186)
3, 12 , 21 , 30 , 39 , . . .
A)
an=6n –9; a20 =111
B)
an=6n –2; a20 =118
C)
an=9n –2; a20 =178
D)
an=9n – 6; a20 =174
Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
187)
36
i = 1
(–4i +8)
187)
A)
–2250
B)
–2376
C)
–2304
D)
–2124
Write a formula for the general term (the nth term) of the geometric sequence.
188)
188)
–8, –16, –32, –64, –128, . . .
A)
an= – 8(2n)
B)
an=a1+2n
C)
an= – 8(2)n
D)
an= – 8(2)n – 1
Solve the problem.
189)
189)
Doctors predict that by administering a vaccine, the number of new cases of a certain childhood
disease will decrease by half each year. If 1100 people were afflicted with the disease in 2012,
estimate the number of new cases in 2017. Round to the nearest whole number.
A)
17 new cases
B)
138 new cases
C)
69 new cases
D)
34 new cases
Find the indicated sum.
190)
10
i =4
12
190)
A)
72
B)
84
C)
588
D)
540
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.
191)
191)
Find a8 when a1=60,000, r = – 0.1.
A)
–0.06
B)
0.0006
C)
0.006
D)
–0.006
Write out the first three terms and the last term of the arithmetic sequence.
192)
8
i=1
(3i – 4)
192)
A)
–4+ 1 + 2 – . . . + 20
B)
–4– 1 + 2 + . . . + 20
C)
–1+ 5 + 23 + . . . + 68
D)
–1+ 2 + 5 + . . . + 20
Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence.
193)
5
i = 1
2·2i
193)
A)
12
B)
124
C)
170
D)
20
Use the formula for the sum of the first n terms of a geometric sequence to solve.
194)
194)
Find the sum of the first 8 terms of the geometric sequence: 5, 10, 20, 40, 80, . . . .
A)
1312
B)
1275
C)
1255
D)
1277
Find the common ratio for the geometric sequence.
195)
195)
7, –0.7, 0.07, –0.007, . . .
A)
0.1
B)
–1
C)
–0.01
D)
–0.1
Write the first four terms of the sequence whose general term is given.
196)
an=3n
(n +3)!
196)
A)
3
7, 9
8, 3, 81
10
B)
3
4, 9
5, 9
2, 81
7
C)
1
8, 3
40 , 3
80 , 9
560
D)
1
8, 3
40 , 3
40 , 9
280
Use the Binomial Theorem to expand the binomial and express the result in simplified form.
197)
(2x + 3)4
197)
A)
48x4+ 288 x3+ 216x2+ 648x + 81
B)
16x3+ 96x2+ 216x + 216
C)
16x4+ 96x3+ 216x2+ 216x + 81
D)
16x4+81x4
Find the common difference for the arithmetic sequence.
198)
198)
3, 5, 7, 9, . . .
A)
6
B)
–2
C)
2
D)
–6
Solve the problem.
199)
199)
As part of her retirement savings plan, Patricia deposited $150 in a bank account during her first
year in the workforce. During each subsequent year, she deposited $35 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.
A)
$815; $19,300
B)
$815; $9650
C)
$850; $20,000
D)
$850; $10,000
Write a formula for the general term (the nth term) of the sequence. Then use the formula for an to find the twelfth
term of the sequence.
200)
200)
3, 12 , 21 , 30 , . . .
A)
an=6n –2; a12 =70
B)
an=9n – 6; a12 =102
C)
an=9n –2; a12 =106
D)
an=6n –9; a12 =63
Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
201)
201)
3+6+9+ . . . +21
A)
7
i = 1
i2
B)
7
i = 1
3i2
C)
7
i = 1
3i
D)
7
i = 0
3i
Evaluate the given binomial coefficient.
202)
6
3
202)
A)
120
B)
20
C)
2
D)
10
Use the Binomial Theorem to expand the binomial and express the result in simplified form.
203)
(4x + 5)3
203)
A)
16x6+ 20x3+ 15,625
B)
16x2+ 40x + 25
C)
64x3+ 240x2+ 300x + 125
D)
64x3+ 240x2+ 240x + 125
Use the formula for the sum of the first n terms of a geometric sequence to solve.
204)
204)
Find the sum of the first four terms of the geometric sequence: –3, –15, –75, . . . .
A)
468
B)
– 468
C)
– 156
D)
–93
Write the first four terms of the sequence whose general term is given.
205)
an=n3
(n – 1)!
205)
A)
1, 8, 27
2, 32
3
B)
3
0, 6
0, 9
2, 2
C)
1
0, 8
0, 27
2, 32
3
D)
3, 6, 9
2, 2