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Math Problems
Algebra 1
Evaluate variable expressions for number sequences
The rule of a certain sequence is
k
=
(
2
n
)
−
1
k=(2n)-1
k
=
(
2
n
)
−
1
. Find the first four terms of the sequence.
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Find the next three numbers in this sequence:
\newline
…
,
3
,
2
,
1
,
0
,
−
1
,
…
\ldots,3,2,1,0,-1,\ldots
…
,
3
,
2
,
1
,
0
,
−
1
,
…
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
2
(
2
)
n
a_n = 2(2)^n
a
n
=
2
(
2
)
n
\newline
_____, _____, _____, _____, _____
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
5
n
+
2
a_n = 5n + 2
a
n
=
5
n
+
2
\newline
_____, _____, _____, _____, _____
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
−
6
n
+
10
a_n = -6n + 10
a
n
=
−
6
n
+
10
\newline
_____, _____, _____, _____, _____
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Find the first four terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
−
10
n
+
4
a_n = -10n + 4
a
n
=
−
10
n
+
4
\newline
_____, _____, _____, _____
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
−
9
n
+
1
a_n = -9n + 1
a
n
=
−
9
n
+
1
\newline
_____, _____, _____, _____, _____
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
−
9
n
+
10
a_n = -9n + 10
a
n
=
−
9
n
+
10
\newline
_____, _____, _____, _____, _____
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
8
n
−
6
a_n = 8n − 6
a
n
=
8
n
−6
\newline
_____, _____, _____, _____, _____
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Find the first three terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
3
n
+
4
a_n = 3n + 4
a
n
=
3
n
+
4
\newline
_____, _____, _____
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Find the first four terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
6
n
−
1
a_n = 6n − 1
a
n
=
6
n
−1
\newline
_____, _____, _____, _____
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
−
10
n
+
2
a_n = -10n + 2
a
n
=
−
10
n
+
2
\newline
_____, _____, _____, _____, _____
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
−
6
n
−
7
a_n = -6n - 7
a
n
=
−
6
n
−
7
\newline
_____, _____, _____, _____, _____
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
4
n
−
6
a_n = 4n − 6
a
n
=
4
n
−6
\newline
_____, _____, _____, _____, _____
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
−
9
n
+
6
a_n = -9n + 6
a
n
=
−
9
n
+
6
\newline
_____, _____, _____, _____, _____
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
−
3
n
a_n = -3n
a
n
=
−
3
n
\newline
_
_
\_\_
__
,
_
_
\_\_
__
,
_
_
\_\_
__
,
_
_
\_\_
__
,
_
_
\_\_
__
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
−
8
n
−
10
a_n = -8n - 10
a
n
=
−
8
n
−
10
\newline
_____, _____, _____, _____, _____
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
8
n
+
7
a_n = 8n + 7
a
n
=
8
n
+
7
\newline
_____, _____, _____, _____, _____
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
−
8
n
−
6
a_n = -8n - 6
a
n
=
−
8
n
−
6
\newline
_____, _____, _____, _____, _____
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
n
−
7
a_n = n - 7
a
n
=
n
−
7
\newline
_____, _____, _____, _____, _____
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
4
n
−
8
a_n = 4n − 8
a
n
=
4
n
−8
\newline
_____, _____, _____, _____, _____
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Find the first three terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
7
n
a_n = 7n
a
n
=
7
n
\newline
___, ___, ____
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Frank opened
3
3
3
boxes of candy. Each box holds
10
10
10
pieces of candy. He shared the pieces equally between him and his friend. How many pieces of candy will each person get?
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Use the given flight data to compute the ground speed, the drift angle, and the course (round your answers to two decimal places). The heading and air speed are
4
5
∘
45^{\circ}
4
5
∘
and
275
m
p
h
275 \mathrm{mph}
275
mph
, respectively, the wind is
50
m
p
h
50 \mathrm{mph}
50
mph
from
13
5
∘
135^{\circ}
13
5
∘
.
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In
△
J
K
L
,
j
=
4.1
c
m
,
l
=
1.2
c
m
\triangle \mathrm{JKL}, j=4.1 \mathrm{~cm}, l=1.2 \mathrm{~cm}
△
JKL
,
j
=
4.1
cm
,
l
=
1.2
cm
and
∠
L
=
2
9
∘
\angle \mathrm{L}=29^{\circ}
∠
L
=
2
9
∘
. Find all possible values of
∠
J
\angle \mathrm{J}
∠
J
, to the nearest
10
10
10
th of a degree.
\newline
Answer:
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In
Δ
U
V
W
,
w
=
5.3
c
m
,
v
=
4.8
c
m
\Delta \mathrm{UVW}, w=5.3 \mathrm{~cm}, v=4.8 \mathrm{~cm}
Δ
UVW
,
w
=
5.3
cm
,
v
=
4.8
cm
and
∠
V
=
15
1
∘
\angle \mathrm{V}=151^{\circ}
∠
V
=
15
1
∘
. Find all possible values of
∠
W
\angle \mathrm{W}
∠
W
, to the nearest
10
10
10
th of a degree.
\newline
Answer:
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In
Δ
G
H
I
,
g
=
9.8
c
m
,
i
=
9.6
c
m
\Delta \mathrm{GHI}, g=9.8 \mathrm{~cm}, i=9.6 \mathrm{~cm}
Δ
GHI
,
g
=
9.8
cm
,
i
=
9.6
cm
and
∠
I
=
4
3
∘
\angle \mathrm{I}=43^{\circ}
∠
I
=
4
3
∘
. Find all possible values of
∠
G
\angle \mathrm{G}
∠
G
, to the nearest
10
10
10
th of a degree.
\newline
Answer:
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In
△
E
F
G
,
e
=
680
c
m
,
g
=
940
c
m
\triangle \mathrm{EFG}, e=680 \mathrm{~cm}, g=940 \mathrm{~cm}
△
EFG
,
e
=
680
cm
,
g
=
940
cm
and
∠
G
=
2
1
∘
\angle \mathrm{G}=21^{\circ}
∠
G
=
2
1
∘
. Find all possible values of
∠
E
\angle \mathrm{E}
∠
E
, to the nearest degree.
\newline
Answer:
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Find all angles,
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
, that satisfy the equation below, to the nearest tenth of a degree.
\newline
−
6
cos
2
θ
−
10
cos
θ
−
1
=
−
3
cos
θ
-6 \cos ^{2} \theta-10 \cos \theta-1=-3 \cos \theta
−
6
cos
2
θ
−
10
cos
θ
−
1
=
−
3
cos
θ
\newline
Answer:
θ
=
\theta=
θ
=
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Find all angles,
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
, that satisfy the equation below, to the nearest tenth of a degree.
\newline
16
cot
2
θ
−
1
=
0
16 \cot ^{2} \theta-1=0
16
cot
2
θ
−
1
=
0
\newline
Answer:
θ
=
\theta=
θ
=
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Find the first four terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
3
n
−
5
a_n = 3n - 5
a
n
=
3
n
−
5
\newline
_____, _____, _____, _____
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Find the first three terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
2
(
4
)
n
a_n = 2(4)^n
a
n
=
2
(
4
)
n
\newline
_
_
\_\_
__
,
_
_
\_\_
__
,
_
_
\_\_
__
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
7
n
+
8
a_n = 7n + 8
a
n
=
7
n
+
8
\newline
_____, _____, _____, _____, _____
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
−
7
n
+
8
a_n = -7n + 8
a
n
=
−
7
n
+
8
\newline
_____, _____, _____, _____, _____
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
10
n
a_n = 10n
a
n
=
10
n
\newline
_____, _____, _____, _____, _____
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
n
+
7
a_n = n + 7
a
n
=
n
+
7
\newline
_____, _____, _____, _____, _____
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
5
n
+
6
a_n = 5n + 6
a
n
=
5
n
+
6
\newline
_____, _____, _____, _____, _____
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
6
n
−
4
a_n = 6n − 4
a
n
=
6
n
−4
\newline
_____, _____, _____, _____, _____
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Find the first three terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
4
n
−
8
a_n = 4n − 8
a
n
=
4
n
−8
\newline
_____, _____, _____
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
n
−
8
a_n = n - 8
a
n
=
n
−
8
\newline
_____, _____, _____, _____, _____
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Find the first four terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
10
n
−
2
a_n = 10n − 2
a
n
=
10
n
−2
\newline
_____, _____, _____, _____
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
4
n
+
8
a_n = 4n + 8
a
n
=
4
n
+
8
\newline
_____, _____, _____, _____, _____
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
−
7
n
+
7
a_n = -7n + 7
a
n
=
−
7
n
+
7
\newline
_____, _____, _____, _____, _____
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
−
9
n
+
5
a_n = -9n + 5
a
n
=
−
9
n
+
5
\newline
_____, _____, _____, _____, _____
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Find the first three terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
7
n
−
6
a_n = 7n − 6
a
n
=
7
n
−6
\newline
_____, _____, _____
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
−
10
n
−
9
a_n = -10n - 9
a
n
=
−
10
n
−
9
\newline
_____, _____, _____, _____, _____
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Find the first three terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
8
n
−
7
a_n = 8n − 7
a
n
=
8
n
−7
\newline
_____, _____, _____
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Find the first four terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
7
n
+
7
a_n = 7n + 7
a
n
=
7
n
+
7
\newline
_____, _____, _____, _____
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
3
(
2
)
n
a_n = 3(2)^n
a
n
=
3
(
2
)
n
\newline
_____, _____, _____, _____, _____
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Find the first five terms of the sequence defined below, where
n
n
n
represents the position of a term in the sequence. Start with
n
=
1
n = 1
n
=
1
.
\newline
a
n
=
4
n
a_n = 4^n
a
n
=
4
n
\newline
_____, _____, _____, _____, _____
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