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Math Problems
Algebra 1
Identify a sequence as explicit or recursive
Which of the following expression(s) are equivalent to
\newline
(
x
2
y
3
)
/
(
x
y
)
(x^{2}y^{3})/(xy)
(
x
2
y
3
)
/
(
x
y
)
? Select all that apply.
\newline
A.
x
y
2
xy^2
x
y
2
\newline
B.
x
y
3
y
\frac{xy^3}{y}
y
x
y
3
\newline
C.
x
2
y
2
x
\frac{x^2y^2}{x}
x
x
2
y
2
\newline
D.
x
3
x
4
x^3x^4
x
3
x
4
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Write an explicit formula that represents the sequence defined by the following recursive formula:
\newline
a
1
=
−
5
and
a
n
=
a
n
−
1
+
3
a_{1}=-5 \text { and } a_{n}=a_{n-1}+3
a
1
=
−
5
and
a
n
=
a
n
−
1
+
3
\newline
Answer:
a
n
=
a_{n}=
a
n
=
Get tutor help
Write an explicit formula that represents the sequence defined by the following recursive formula:
\newline
a
1
=
−
10
and
a
n
=
a
n
−
1
+
6
a_{1}=-10 \text { and } a_{n}=a_{n-1}+6
a
1
=
−
10
and
a
n
=
a
n
−
1
+
6
\newline
Answer:
a
n
=
a_{n}=
a
n
=
Get tutor help
Write an explicit formula that represents the sequence defined by the following recursive formula:
\newline
a
1
=
−
4
and
a
n
=
a
n
−
1
+
2
a_{1}=-4 \text { and } a_{n}=a_{n-1}+2
a
1
=
−
4
and
a
n
=
a
n
−
1
+
2
\newline
Answer:
a
n
=
a_{n}=
a
n
=
Get tutor help
Write an explicit formula that represents the sequence defined by the following recursive formula:
\newline
a
1
=
5
and
a
n
=
a
n
−
1
−
3
a_{1}=5 \text { and } a_{n}=a_{n-1}-3
a
1
=
5
and
a
n
=
a
n
−
1
−
3
\newline
Answer:
a
n
=
a_{n}=
a
n
=
Get tutor help
Write an explicit formula that represents the sequence defined by the following recursive formula:
\newline
a
1
=
5
and
a
n
=
a
n
−
1
+
3
a_{1}=5 \text { and } a_{n}=a_{n-1}+3
a
1
=
5
and
a
n
=
a
n
−
1
+
3
\newline
Answer:
a
n
=
a_{n}=
a
n
=
Get tutor help
Find the
9
9
9
th term of the arithmetic sequence
−
2
x
−
5
,
−
5
x
−
8
,
−
8
x
−
11
,
…
-2 x-5,-5 x-8,-8 x-11, \ldots
−
2
x
−
5
,
−
5
x
−
8
,
−
8
x
−
11
,
…
\newline
Answer:
Get tutor help
Find the
12
12
12
th term of the geometric sequence shown below.
\newline
10
x
4
,
−
10
x
7
,
10
x
10
,
…
10 x^{4},-10 x^{7}, 10 x^{10}, \ldots
10
x
4
,
−
10
x
7
,
10
x
10
,
…
\newline
Answer:
Get tutor help
Find the
82
n
d
82 n d
82
n
d
term of the arithmetic sequence
−
27
,
−
43
,
−
59
,
…
-27,-43,-59, \ldots
−
27
,
−
43
,
−
59
,
…
\newline
Answer:
Get tutor help
Which recursive sequence would produce the sequence
9
,
−
32
,
91
,
…
9,-32,91, \ldots
9
,
−
32
,
91
,
…
?
\newline
a
1
=
9
a_{1}=9
a
1
=
9
and
a
n
=
−
3
a
n
−
1
−
5
a_{n}=-3 a_{n-1}-5
a
n
=
−
3
a
n
−
1
−
5
\newline
a
1
=
9
a_{1}=9
a
1
=
9
and
a
n
=
−
4
a
n
−
1
+
4
a_{n}=-4 a_{n-1}+4
a
n
=
−
4
a
n
−
1
+
4
\newline
a
1
=
9
a_{1}=9
a
1
=
9
and
a
n
=
−
5
a
n
−
1
−
3
a_{n}=-5 a_{n-1}-3
a
n
=
−
5
a
n
−
1
−
3
\newline
a
1
=
9
a_{1}=9
a
1
=
9
and
a
n
=
4
a
n
−
1
−
4
a_{n}=4 a_{n-1}-4
a
n
=
4
a
n
−
1
−
4
Get tutor help
Which recursive sequence would produce the sequence
8
,
−
28
,
80
,
…
8,-28,80, \ldots
8
,
−
28
,
80
,
…
?
\newline
a
1
=
8
a_{1}=8
a
1
=
8
and
a
n
=
−
4
a
n
−
1
−
3
a_{n}=-4 a_{n-1}-3
a
n
=
−
4
a
n
−
1
−
3
\newline
a
1
=
8
a_{1}=8
a
1
=
8
and
a
n
=
−
3
a
n
−
1
−
4
a_{n}=-3 a_{n-1}-4
a
n
=
−
3
a
n
−
1
−
4
\newline
a
1
=
8
a_{1}=8
a
1
=
8
and
a
n
=
4
a
n
−
1
−
4
a_{n}=4 a_{n-1}-4
a
n
=
4
a
n
−
1
−
4
\newline
a
1
=
8
a_{1}=8
a
1
=
8
and
a
n
=
−
4
a
n
−
1
+
4
a_{n}=-4 a_{n-1}+4
a
n
=
−
4
a
n
−
1
+
4
Get tutor help
Which recursive sequence would produce the sequence
5
,
−
11
,
37
,
…
5,-11,37, \ldots
5
,
−
11
,
37
,
…
?
\newline
a
1
=
5
a_{1}=5
a
1
=
5
and
a
n
=
−
a
n
−
1
−
2
a_{n}=-a_{n-1}-2
a
n
=
−
a
n
−
1
−
2
\newline
a
1
=
5
a_{1}=5
a
1
=
5
and
a
n
=
−
3
a
n
−
1
+
4
a_{n}=-3 a_{n-1}+4
a
n
=
−
3
a
n
−
1
+
4
\newline
a
1
=
5
a_{1}=5
a
1
=
5
and
a
n
=
−
2
a
n
−
1
−
1
a_{n}=-2 a_{n-1}-1
a
n
=
−
2
a
n
−
1
−
1
\newline
a
1
=
5
a_{1}=5
a
1
=
5
and
a
n
=
4
a
n
−
1
−
3
a_{n}=4 a_{n-1}-3
a
n
=
4
a
n
−
1
−
3
Get tutor help
Which recursive sequence would produce the sequence
3
,
−
19
,
91
,
…
3,-19,91, \ldots
3
,
−
19
,
91
,
…
?
\newline
a
1
=
3
a_{1}=3
a
1
=
3
and
a
n
=
−
6
a
n
−
1
−
1
a_{n}=-6 a_{n-1}-1
a
n
=
−
6
a
n
−
1
−
1
\newline
a
1
=
3
a_{1}=3
a
1
=
3
and
a
n
=
−
5
a
n
−
1
−
4
a_{n}=-5 a_{n-1}-4
a
n
=
−
5
a
n
−
1
−
4
\newline
a
1
=
3
a_{1}=3
a
1
=
3
and
a
n
=
−
a
n
−
1
−
6
a_{n}=-a_{n-1}-6
a
n
=
−
a
n
−
1
−
6
\newline
a
1
=
3
a_{1}=3
a
1
=
3
and
a
n
=
−
4
a
n
−
1
−
5
a_{n}=-4 a_{n-1}-5
a
n
=
−
4
a
n
−
1
−
5
Get tutor help
Which recursive sequence would produce the sequence
7
,
−
33
,
167
,
…
7,-33,167, \ldots
7
,
−
33
,
167
,
…
?
\newline
a
1
=
7
a_{1}=7
a
1
=
7
and
a
n
=
2
a
n
−
1
−
5
a_{n}=2 a_{n-1}-5
a
n
=
2
a
n
−
1
−
5
\newline
a
1
=
7
a_{1}=7
a
1
=
7
and
a
n
=
−
5
a
n
−
1
+
2
a_{n}=-5 a_{n-1}+2
a
n
=
−
5
a
n
−
1
+
2
\newline
a
1
=
7
a_{1}=7
a
1
=
7
and
a
n
=
−
4
a
n
−
1
−
5
a_{n}=-4 a_{n-1}-5
a
n
=
−
4
a
n
−
1
−
5
\newline
a
1
=
7
a_{1}=7
a
1
=
7
and
a
n
=
−
5
a
n
−
1
−
4
a_{n}=-5 a_{n-1}-4
a
n
=
−
5
a
n
−
1
−
4
Get tutor help
Which recursive sequence would produce the sequence
2
,
8
,
26
,
…
2,8,26, \ldots
2
,
8
,
26
,
…
?
\newline
a
1
=
2
a_{1}=2
a
1
=
2
and
a
n
=
3
a
n
−
1
+
2
a_{n}=3 a_{n-1}+2
a
n
=
3
a
n
−
1
+
2
\newline
a
1
=
2
a_{1}=2
a
1
=
2
and
a
n
=
2
a
n
−
1
+
3
a_{n}=2 a_{n-1}+3
a
n
=
2
a
n
−
1
+
3
\newline
a
1
=
2
a_{1}=2
a
1
=
2
and
a
n
=
4
a
n
−
1
+
2
a_{n}=4 a_{n-1}+2
a
n
=
4
a
n
−
1
+
2
\newline
a
1
=
2
a_{1}=2
a
1
=
2
and
a
n
=
2
a
n
−
1
+
4
a_{n}=2 a_{n-1}+4
a
n
=
2
a
n
−
1
+
4
Get tutor help
Which recursive sequence would produce the sequence
5
,
−
21
,
109
,
…
5,-21,109, \ldots
5
,
−
21
,
109
,
…
?
\newline
a
1
=
5
a_{1}=5
a
1
=
5
and
a
n
=
−
a
n
−
1
−
4
a_{n}=-a_{n-1}-4
a
n
=
−
a
n
−
1
−
4
\newline
a
1
=
5
a_{1}=5
a
1
=
5
and
a
n
=
4
a
n
−
1
−
5
a_{n}=4 a_{n-1}-5
a
n
=
4
a
n
−
1
−
5
\newline
a
1
=
5
a_{1}=5
a
1
=
5
and
a
n
=
−
5
a
n
−
1
+
4
a_{n}=-5 a_{n-1}+4
a
n
=
−
5
a
n
−
1
+
4
\newline
a
1
=
5
a_{1}=5
a
1
=
5
and
a
n
=
−
4
a
n
−
1
−
1
a_{n}=-4 a_{n-1}-1
a
n
=
−
4
a
n
−
1
−
1
Get tutor help
Which recursive sequence would produce the sequence
6
,
−
33
,
162
,
…
6,-33,162, \ldots
6
,
−
33
,
162
,
…
?
\newline
a
1
=
6
a_{1}=6
a
1
=
6
and
a
n
=
3
a
n
−
1
−
6
a_{n}=3 a_{n-1}-6
a
n
=
3
a
n
−
1
−
6
\newline
a
1
=
6
a_{1}=6
a
1
=
6
and
a
n
=
−
5
a
n
−
1
−
3
a_{n}=-5 a_{n-1}-3
a
n
=
−
5
a
n
−
1
−
3
\newline
a
1
=
6
a_{1}=6
a
1
=
6
and
a
n
=
−
6
a
n
−
1
+
3
a_{n}=-6 a_{n-1}+3
a
n
=
−
6
a
n
−
1
+
3
\newline
a
1
=
6
a_{1}=6
a
1
=
6
and
a
n
=
−
3
a
n
−
1
−
5
a_{n}=-3 a_{n-1}-5
a
n
=
−
3
a
n
−
1
−
5
Get tutor help
Let
f
f
f
be a continuous function on the closed interval
[
−
2
,
1
]
[-2,1]
[
−
2
,
1
]
, where
f
(
−
2
)
=
3
f(-2)=3
f
(
−
2
)
=
3
and
f
(
1
)
=
6
f(1)=6
f
(
1
)
=
6
.
\newline
Which of the following is guaranteed by the Intermediate Value Theorem?
\newline
Choose
1
1
1
answer:
\newline
(A)
f
(
c
)
=
0
f(c)=0
f
(
c
)
=
0
for at least one
c
c
c
between
−
2
-2
−
2
and
1
1
1
\newline
(B)
f
(
c
)
=
4
f(c)=4
f
(
c
)
=
4
for at least one
c
c
c
between
−
2
-2
−
2
and
1
1
1
\newline
(C)
f
(
c
)
=
0
f(c)=0
f
(
c
)
=
0
for at least one
c
c
c
between
3
3
3
and
6
6
6
\newline
(D)
f
(
c
)
=
4
f(c)=4
f
(
c
)
=
4
for at least one
c
c
c
between
3
3
3
and
6
6
6
Get tutor help
Let
h
h
h
be a continuous function on the closed interval
[
−
3
,
4
]
[-3,4]
[
−
3
,
4
]
, where
h
(
−
3
)
=
−
1
h(-3)=-1
h
(
−
3
)
=
−
1
and
h
(
4
)
=
2
h(4)=2
h
(
4
)
=
2
.
\newline
Which of the following is guaranteed by the Intermediate Value Theorem?
\newline
Choose
1
1
1
answer:
\newline
(A)
h
(
c
)
=
1
h(c)=1
h
(
c
)
=
1
for at least one
c
c
c
between
−
1
-1
−
1
and
2
2
2
\newline
(B)
h
(
c
)
=
1
h(c)=1
h
(
c
)
=
1
for at least one
c
c
c
between
−
3
-3
−
3
and
4
4
4
\newline
(C)
h
(
c
)
=
−
2
h(c)=-2
h
(
c
)
=
−
2
for at least one
c
c
c
between
−
3
-3
−
3
and
4
4
4
\newline
(D)
h
(
c
)
=
−
2
h(c)=-2
h
(
c
)
=
−
2
for at least one
c
c
c
between
−
1
-1
−
1
and
2
2
2
Get tutor help
Let
g
g
g
be a continuous function on the closed interval
[
−
3
,
3
]
[-3,3]
[
−
3
,
3
]
, where
g
(
−
3
)
=
0
g(-3)=0
g
(
−
3
)
=
0
and
g
(
3
)
=
6
g(3)=6
g
(
3
)
=
6
.
\newline
Which of the following is guaranteed by the Intermediate Value Theorem?
\newline
Choose
1
1
1
answer:
\newline
(A)
g
(
c
)
=
−
2
g(c)=-2
g
(
c
)
=
−
2
for at least one
c
c
c
between
−
3
-3
−
3
and
3
3
3
\newline
(B)
g
(
c
)
=
−
2
g(c)=-2
g
(
c
)
=
−
2
for at least one
c
c
c
between
0
0
0
and
6
6
6
\newline
(C)
g
(
c
)
=
5
g(c)=5
g
(
c
)
=
5
for at least one
c
c
c
between
0
0
0
and
6
6
6
\newline
(D)
g
(
c
)
=
5
g(c)=5
g
(
c
)
=
5
for at least one
c
c
c
between
−
3
-3
−
3
and
3
3
3
Get tutor help
Consider the expression
\newline
a
+
(
b
+
1
)
+
2
c
.
a+(b+1)+2 c \text {. }
a
+
(
b
+
1
)
+
2
c
.
\newline
Complete
2
2
2
descriptions of the parts of the expression.
\newline
1
1
1
. The entire expression is a sum with
□
\square
□
.
\newline
2
2
2
. On its own,
2
c
2 c
2
c
is a product with
□
\square
□
.
Get tutor help
Consider the expression
\newline
1
2
x
2
+
x
+
7
.
\frac{1}{2} x^{2}+x+7 \text {. }
2
1
x
2
+
x
+
7
.
\newline
Complete
2
2
2
descriptions of the parts of the expression.
\newline
1
1
1
. The entire expression is a sum with
□
\square
□
.
\newline
2
2
2
. The coefficients are
□
\square
□
.
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An arithmetic sequence is defined as follows:
\newline
{
a
1
=
−
29
a
i
=
a
i
−
1
+
2
\left\{\begin{array}{l} a_{1}=-29 \\ a_{i}=a_{i-1}+2 \end{array}\right.
{
a
1
=
−
29
a
i
=
a
i
−
1
+
2
\newline
Find the sum of the first
48
48
48
terms in the sequence.
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An arithmetic sequence is defined as follows:
\newline
{
a
1
=
89
a
i
=
a
i
−
1
−
9
\left\{\begin{array}{l} a_{1}=89 \\ a_{i}=a_{i-1}-9 \end{array}\right.
{
a
1
=
89
a
i
=
a
i
−
1
−
9
\newline
Find the sum of the first
33
33
33
terms in the sequence.
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An arithmetic sequence is defined as follows:
\newline
{
a
1
=
49
a
i
=
a
i
−
1
−
3
\left\{\begin{array}{l} a_{1}=49 \\ a_{i}=a_{i-1}-3 \end{array}\right.
{
a
1
=
49
a
i
=
a
i
−
1
−
3
\newline
Find the sum of the first
26
26
26
terms in the sequence.
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The geometric sequence
a
i
a_{i}
a
i
is defined by the formula:
\newline
a
1
=
8
a
i
=
a
i
−
1
⋅
(
−
1.5
)
\begin{array}{l} a_{1}=8 \\ a_{i}=a_{i-1} \cdot(-1.5) \end{array}
a
1
=
8
a
i
=
a
i
−
1
⋅
(
−
1.5
)
\newline
Find the sum of the first
20
20
20
terms in the sequence.
\newline
Choose
1
1
1
answer:
\newline
(A)
−
2.47
⋅
1
0
17
-2.47 \cdot 10^{17}
−
2.47
⋅
1
0
17
\newline
(B)
−
53
,
220.11
-53,220.11
−
53
,
220.11
\newline
(C)
−
17
,
734.70
-17,734.70
−
17
,
734.70
\newline
(D)
−
10
,
637.62
-10,637.62
−
10
,
637.62
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What happens to the value of the expression
m
−
10
m-10
m
−
10
as
m
m
m
decreases?
\newline
Choose
1
1
1
answer:
\newline
(A) It increases.
\newline
(B) It decreases.
\newline
(C) It stays the same.
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What happens to the value of the expression
70
−
3
g
70-3 g
70
−
3
g
as
g
g
g
increases?
\newline
Choose
1
1
1
answer:
\newline
(A) It increases.
\newline
(B) It decreases.
\newline
(C) It stays the same.
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Solve for
x
x
x
:
\newline
−
1
6
x
=
5
-\frac{1}{6}x=5
−
6
1
x
=
5
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Which word best describes this formula for the sequence
a
n
a_n
a
n
?
\newline
a
n
=
−
6
(
−
1
/
7
)
(
n
+
4
)
+
1
a_n = -6(-1/7)^{(n + 4)} + 1
a
n
=
−
6
(
−
1/7
)
(
n
+
4
)
+
1
\newline
Choices:
\newline
[A]explicit
\text{[A]explicit}
[A]explicit
\newline
[B]recursive
\text{[B]recursive}
[B]recursive
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