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Math Problems
Precalculus
Find the sum of a finite geometric series
In how many different ways can the letters of the word
THOUGHTS
\text{THOUGHTS}
THOUGHTS
be arranged so that the vowels always come together?
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Analyze the map below and answer the question that follows.
\newline
List the six regions outlined on the map above.
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A spinner is divided into
5
5
5
equal sections. When the spinner is spun, what is the probability of the events listed below?
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What is the image point of
(
−
2
,
6
)
(-2,6)
(
−
2
,
6
)
after a translation left
2
2
2
units and up
4
4
4
units?
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Write
2730
2730
2730
as a product of prime factors.
\newline
Enter your answer as a product of prime numbers, like
\newline
2
×
3
2\times3
2
×
3
, or as a single prime number, like
17
17
17
.
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Find the sum of the first
7
7
7
terms in the following geometric series. Do not round your answer.
1024
+
512
+
256
+
…
1024+512+256+\ldots
1024
+
512
+
256
+
…
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In a geometric sequence, the first term,
a
1
a_{1}
a
1
, is equal to
8
8
8
, and the third term,
a
3
a_{3}
a
3
, is equal to
200
200
200
. Which number represents the common ratio of the geometric sequence?
\newline
r
=
3
r=3
r
=
3
\newline
r
=
4
r=4
r
=
4
\newline
r
=
5
r=5
r
=
5
\newline
r
=
6
r=6
r
=
6
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In a geometric sequence, the first term,
a
1
a_{1}
a
1
, is equal to
2
2
2
, and the fourth term,
a
4
a_{4}
a
4
, is equal to
128
128
128
. Which number represents the common ratio of the geometric sequence?
\newline
r
=
1
r=1
r
=
1
\newline
r
=
2
r=2
r
=
2
\newline
r
=
3
r=3
r
=
3
\newline
r
=
4
r=4
r
=
4
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In a geometric sequence, the first term,
a
1
a_{1}
a
1
, is equal to
7
7
7
, and the fifth term,
a
5
a_{5}
a
5
, is equal to
112
112
112
. Which number represents the common ratio of the geometric sequence?
\newline
r
=
1
r=1
r
=
1
\newline
r
=
2
r=2
r
=
2
\newline
r
=
3
r=3
r
=
3
\newline
r
=
4
r=4
r
=
4
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In a geometric sequence, the first term,
a
1
a_{1}
a
1
, is equal to
2
2
2
, and the third term,
a
3
a_{3}
a
3
, is equal to
72
72
72
. Which number represents the common ratio of the geometric sequence?
\newline
r
=
6
r=6
r
=
6
\newline
r
=
7
r=7
r
=
7
\newline
r
=
8
r=8
r
=
8
\newline
r
=
9
r=9
r
=
9
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In a geometric sequence, the first term,
a
1
a_{1}
a
1
, is equal to
6
6
6
, and the third term,
a
3
a_{3}
a
3
, is equal to
96
96
96
. Which number represents the common ratio of the geometric sequence?
\newline
r
=
3
r=3
r
=
3
\newline
r
=
4
r=4
r
=
4
\newline
r
=
5
r=5
r
=
5
\newline
r
=
6
r=6
r
=
6
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In a geometric sequence, the first term,
a
1
a_{1}
a
1
, is equal to
8
8
8
, and the third term,
a
3
a_{3}
a
3
, is equal to
72
72
72
. Which number represents the common ratio of the geometric sequence?
\newline
r
=
2
r=2
r
=
2
\newline
r
=
3
r=3
r
=
3
\newline
r
=
4
r=4
r
=
4
\newline
r
=
5
r=5
r
=
5
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In a geometric sequence, the first term,
a
1
a_{1}
a
1
, is equal to
1
1
1
, and the fourth term,
a
4
a_{4}
a
4
, is equal to
64
64
64
. Which number represents the common ratio of the geometric sequence?
\newline
r
=
2
r=2
r
=
2
\newline
r
=
3
r=3
r
=
3
\newline
r
=
4
r=4
r
=
4
\newline
r
=
5
r=5
r
=
5
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In a geometric sequence, the first term,
a
1
a_{1}
a
1
, is equal to
1
1
1
, and the third term,
a
3
a_{3}
a
3
, is equal to
9
9
9
. Which number represents the common ratio of the geometric sequence?
\newline
r
=
2
r=2
r
=
2
\newline
r
=
3
r=3
r
=
3
\newline
r
=
4
r=4
r
=
4
\newline
r
=
5
r=5
r
=
5
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In a geometric sequence, the first term,
a
1
a_{1}
a
1
, is equal to
3
3
3
, and the fifth term,
a
5
a_{5}
a
5
, is equal to
48
48
48
. Which number represents the common ratio of the geometric sequence?
\newline
r
=
1
r=1
r
=
1
\newline
r
=
2
r=2
r
=
2
\newline
r
=
3
r=3
r
=
3
\newline
r
=
4
r=4
r
=
4
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In a geometric sequence, the first term,
a
1
a_{1}
a
1
, is equal to
1
1
1
, and the third term,
a
3
a_{3}
a
3
, is equal to
36
36
36
. Which number represents the common ratio of the geometric sequence?
\newline
r
=
3
r=3
r
=
3
\newline
r
=
4
r=4
r
=
4
\newline
r
=
5
r=5
r
=
5
\newline
r
=
6
r=6
r
=
6
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