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Let’s check out your problem:
Solve for
x
x
x
.
\newline
−
5
7
+
7
x
=
9
7
x
\frac{-5}{7}+\frac{7}{x}=\frac{9}{7 x}
7
−
5
+
x
7
=
7
x
9
\newline
Answer:
x
=
x=
x
=
View step-by-step help
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Math Problems
Algebra 2
Partial sums of arithmetic series
Full solution
Q.
Solve for
x
x
x
.
\newline
−
5
7
+
7
x
=
9
7
x
\frac{-5}{7}+\frac{7}{x}=\frac{9}{7 x}
7
−
5
+
x
7
=
7
x
9
\newline
Answer:
x
=
x=
x
=
Write Equation:
Write down the equation.
\newline
rac{-5}{7} + rac{7}{x} = rac{9}{7x}
Find Common Denominator:
Find a common denominator for the terms on the left side of the equation, which is
7
x
7x
7
x
.
−
5
x
7
x
+
49
7
x
=
9
7
x
\frac{-5x}{7x} + \frac{49}{7x} = \frac{9}{7x}
7
x
−
5
x
+
7
x
49
=
7
x
9
Combine Fractions:
Combine the
fractions
on the left side of the equation.
(
−
5
x
)
+
49
7
x
=
9
7
x
\frac{{(-5x) + 49}}{{7x}} = \frac{9}{{7x}}
7
x
(
−
5
x
)
+
49
=
7
x
9
Set Numerators Equal:
Since the denominators are the same, we can set the numerators equal to each other.
\newline
−
5
x
+
49
=
9
-5x + 49 = 9
−
5
x
+
49
=
9
Subtract and Isolate:
Subtract
49
49
49
from both sides of the equation to isolate the term with
x
x
x
.
\newline
−
5
x
+
49
−
49
=
9
−
49
-5x + 49 - 49 = 9 - 49
−
5
x
+
49
−
49
=
9
−
49
\newline
−
5
x
=
−
40
-5x = -40
−
5
x
=
−
40
Divide to Solve:
Divide both sides of the equation by
−
5
-5
−
5
to solve for
x
x
x
.
x
=
−
40
−
5
x = \frac{-40}{-5}
x
=
−
5
−
40
x
=
8
x = 8
x
=
8
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Find the sum of the finite arithmetic series.
∑
n
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1
10
(
7
n
+
4
)
\sum_{n=1}^{10} (7n+4)
∑
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What kind of sequence is this?
2
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…
2, 10, 50, 250, \ldots
2
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10
,
50
,
250
,
…
Choices:Choices:
\newline
[A]arithmetic
\text{[A]arithmetic}
[A]arithmetic
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[B]geometric
\text{[B]geometric}
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[C]both
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[D]neither
\text{[D]neither}
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What is the missing number in this pattern?
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81
,
_
_
_
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1, 4, 9, 16, 25, 36, 49, 64, 81, \_\_\_\_
1
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4
,
9
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25
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Question
Classify the series.
∑
n
=
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(
n
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2
)
3
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∑
n
=
0
12
(
n
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)
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\newline
Choices:
\newline
[A]arithmetic
\text{[A]arithmetic}
[A]arithmetic
\newline
[B]geometric
\text{[B]geometric}
[B]geometric
\newline
[C]both
\text{[C]both}
[C]both
\newline
[D]neither
\text{[D]neither}
[D]neither
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Question
Find the first three partial sums of the series.
\newline
1
+
6
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11
+
16
+
21
+
26
+
⋯
1 + 6 + 11 + 16 + 21 + 26 + \cdots
1
+
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11
+
16
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21
+
26
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\newline
Write your answers as integers or fractions in simplest form.
\newline
S
1
=
S_1 =
S
1
=
____
\newline
S
2
=
S_2 =
S
2
=
____
\newline
S
3
=
S_3 =
S
3
=
____
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Question
Find the third partial sum of the series.
\newline
3
+
9
+
15
+
21
+
27
+
33
+
⋯
3 + 9 + 15 + 21 + 27 + 33 + \cdots
3
+
9
+
15
+
21
+
27
+
33
+
⋯
\newline
Write your answer as an integer or a fraction in simplest form.
\newline
S
3
=
S_3 =
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3
=
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Question
Find the first three partial sums of the series.
\newline
1
+
7
+
13
+
19
+
25
+
31
+
⋯
1 + 7 + 13 + 19 + 25 + 31 + \cdots
1
+
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+
13
+
19
+
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+
31
+
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\newline
Write your answers as integers or fractions in simplest form.
\newline
S
1
=
S_1 =
S
1
=
____
\newline
S
2
=
S_2 =
S
2
=
____
\newline
S
3
=
S_3 =
S
3
=
____
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Question
Does the infinite geometric series converge or diverge?
\newline
1
+
3
4
+
9
16
+
27
64
+
⋯
1 + \frac{3}{4} + \frac{9}{16} + \frac{27}{64} + \cdots
1
+
4
3
+
16
9
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+
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\newline
Choices:
\newline
[A]converge
\text{[A]converge}
[A]converge
\newline
[B]diverge
\text{[B]diverge}
[B]diverge
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