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Luas tanah Pak Hasan
400
m
2
400\,\text{m}^2
400
m
2
,
1
4
\frac{1}{4}
4
1
lahan tersebut ditanami singkong,
5
8
\frac{5}{8}
8
5
ditanami sayuran. Luas sisa kebun Pak Hasan adalah....
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Math Problems
Precalculus
Introduction to sigma notation
Full solution
Q.
Luas tanah Pak Hasan
400
m
2
400\,\text{m}^2
400
m
2
,
1
4
\frac{1}{4}
4
1
lahan tersebut ditanami singkong,
5
8
\frac{5}{8}
8
5
ditanami sayuran. Luas sisa kebun Pak Hasan adalah....
Calculate Cassava Area:
First, calculate the area planted with cassava:
1
4
\frac{1}{4}
4
1
of
400
m
2
400\,\text{m}^2
400
m
2
.
\newline
1
4
×
400
=
100
m
2
\frac{1}{4} \times 400 = 100\,\text{m}^2
4
1
×
400
=
100
m
2
.
Calculate Vegetable Area:
Next, calculate the area planted with vegetables:
5
8
\frac{5}{8}
8
5
of
400
m
2
400\,\text{m}^2
400
m
2
.
\newline
5
8
×
400
=
250
m
2
\frac{5}{8} \times 400 = 250\,\text{m}^2
8
5
×
400
=
250
m
2
.
Find Total Planted Area:
Now, add the areas of cassava and vegetables to find the total planted area.
100
m
2
+
250
m
2
=
350
m
2
100\,\text{m}^2 + 250\,\text{m}^2 = 350\,\text{m}^2
100
m
2
+
250
m
2
=
350
m
2
.
Find Remaining Area:
Finally, subtract the total planted area from the total land area to find the remaining area.
400
m
2
−
350
m
2
=
50
m
2
400\,\text{m}^2 - 350\,\text{m}^2 = 50\,\text{m}^2
400
m
2
−
350
m
2
=
50
m
2
.
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Find the sum of the finite arithmetic series.
∑
n
=
1
10
(
7
n
+
4
)
\sum_{n=1}^{10} (7n+4)
∑
n
=
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10
(
7
n
+
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)
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______
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What kind of sequence is this?
2
,
10
,
50
,
250
,
…
2, 10, 50, 250, \ldots
2
,
10
,
50
,
250
,
…
Choices: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}
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What is the missing number in this pattern?
1
,
4
,
9
,
16
,
25
,
36
,
49
,
64
,
81
,
_
_
_
_
1, 4, 9, 16, 25, 36, 49, 64, 81, \_\_\_\_
1
,
4
,
9
,
16
,
25
,
36
,
49
,
64
,
81
,
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Classify the series.
∑
n
=
0
12
(
n
+
2
)
3
\sum_{n = 0}^{12} (n + 2)^3
∑
n
=
0
12
(
n
+
2
)
3
\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
+
11
+
16
+
21
+
26
+
⋯
1 + 6 + 11 + 16 + 21 + 26 + \cdots
1
+
6
+
11
+
16
+
21
+
26
+
⋯
\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 =
S
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
+
7
+
13
+
19
+
25
+
31
+
⋯
\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
+
64
27
+
⋯
\newline
Choices:
\newline
[A]converge
\text{[A]converge}
[A]converge
\newline
[B]diverge
\text{[B]diverge}
[B]diverge
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