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Math Problems
Algebra 1
Evaluate variable expressions for number sequences
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
+
10
a_n = -5n + 10
a
n
=
−
5
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
=
−
5
n
−
5
a_n = -5n - 5
a
n
=
−
5
n
−
5
\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
−
2
a_n = 6n − 2
a
n
=
6
n
−2
\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
−
9
a_n = 4n − 9
a
n
=
4
n
−9
\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
=
2
(
3
)
n
a_n = 2(3)^n
a
n
=
2
(
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
=
10
n
−
2
a_n = 10n − 2
a
n
=
10
n
−2
\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
=
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
=
−
5
n
+
4
a_n = -5n + 4
a
n
=
−
5
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
=
8
n
−
5
a_n = 8n − 5
a
n
=
8
n
−5
\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
(
2
)
n
a_n = 4(2)^n
a
n
=
4
(
2
)
n
\newline
_____, _____, _____, _____, _____
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Given the following point on the unit circle, find the angle, to the nearest tenth of a degree (if necessary), of the terminal side through that point,
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
.
\newline
P
=
(
6
4
,
−
10
4
)
P=\left(\frac{\sqrt{6}}{4},-\frac{\sqrt{10}}{4}\right)
P
=
(
4
6
,
−
4
10
)
\newline
Answer:
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c
(
n
)
=
−
6
+
5
(
n
−
1
)
c(n) = -6 + 5(n - 1)
c
(
n
)
=
−
6
+
5
(
n
−
1
)
\newline
Find the
8
th
8^{\text{th}}
8
th
term in the sequence.
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Write the first four non-zero terms of the power series for
f
(
x
)
=
3
x
cos
(
2
x
5
)
−
6
f(x)=3 x \cos \left(2 x^{5}\right)-6
f
(
x
)
=
3
x
cos
(
2
x
5
)
−
6
about
x
=
0
x=0
x
=
0
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Find the sum of the first
7
7
7
terms of the following series, to the nearest integer.
\newline
6
,
9
,
27
2
,
…
6,9, \frac{27}{2}, \ldots
6
,
9
,
2
27
,
…
\newline
Answer:
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Find the
12
12
12
th term of the geometric sequence shown below.
\newline
6
x
6
,
−
30
x
11
,
150
x
16
,
…
6 x^{6},-30 x^{11}, 150 x^{16}, \ldots
6
x
6
,
−
30
x
11
,
150
x
16
,
…
\newline
Answer:
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Given that events A and B are independent with
P
(
A
)
=
0.92
P(A)=0.92
P
(
A
)
=
0.92
and
P
(
B
)
=
0.15
P(B)=0.15
P
(
B
)
=
0.15
, determine the value of
P
(
B
∣
A
)
P(B \mid A)
P
(
B
∣
A
)
, rounding to the nearest thousandth, if necessary.
\newline
Answer:
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Find the
99
99
99
th term of the arithmetic sequence
−
4
,
7
,
18
,
…
-4,7,18, \ldots
−
4
,
7
,
18
,
…
\newline
Answer:
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Write an explicit formula for
a
n
a_{n}
a
n
, the
n
th
n^{\text {th }}
n
th
term of the sequence
9
,
14
,
19
,
…
9,14,19, \ldots
9
,
14
,
19
,
…
\newline
Answer:
a
n
=
a_{n}=
a
n
=
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The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth (if necessary).
\newline
13
,
26
,
52
,
…
13,26,52, \ldots
13
,
26
,
52
,
…
\newline
Find the
6
6
6
th term.
\newline
Answer:
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The derivative of the function
f
f
f
is defined by
f
′
(
x
)
=
x
2
−
1
+
3
cos
(
2
x
)
f^{\prime}(x)=x^{2}-1+3 \cos (2 x)
f
′
(
x
)
=
x
2
−
1
+
3
cos
(
2
x
)
for
−
1.5
<
x
<
2
-1.5<x<2
−
1.5
<
x
<
2
. Find all intervals in the given domain where the function
f
f
f
is concave down. You may use a calculator and round all values to
3
3
3
decimal places.
\newline
Answer:
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Samuel is the middle of three siblings whose ages are consecutive odd integers. If the sum of their ages is
81
81
81
, find Samuel's age.
\newline
Answer:
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Find the first
4
4
4
non-zero terms of the Taylor polynomial centered at
x
=
0
x=0
x
=
0
for
f
(
x
)
=
cos
6
x
f(x)=\cos 6x
f
(
x
)
=
cos
6
x
.
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The common ratio in a geometric series is
4
4
4
and the first term is
3
3
3
.
\newline
Find the sum of the first
8
8
8
terms in the series.
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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
a_n = -8n
a
n
=
−
8
n
\newline
_
_
_
_
\_\_\_\_
____
,
_
_
_
_
\_\_\_\_
____
,
_
_
_
_
\_\_\_\_
____
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