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Let’s check out your problem:
Solve the formula
A
=
1
2
h
(
a
+
b
)
A=\frac{1}{2} h(a+b)
A
=
2
1
h
(
a
+
b
)
for
a
a
a
View step-by-step help
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Math Problems
Grade 7
Write variable expressions for arithmetic sequences
Full solution
Q.
Solve the formula
A
=
1
2
h
(
a
+
b
)
A=\frac{1}{2} h(a+b)
A
=
2
1
h
(
a
+
b
)
for
a
a
a
Multiply by
2
2
2
:
First, let's isolate the term with
a
a
a
by multiplying both sides of the equation by
2
2
2
to get rid of the fraction.
\newline
2
A
=
h
(
a
+
b
)
2A = h(a + b)
2
A
=
h
(
a
+
b
)
Divide by h:
Now, we divide both sides by
h
h
h
to isolate
(
a
+
b
)
(a + b)
(
a
+
b
)
.
\newline
2
A
h
=
a
+
b
\frac{2A}{h} = a + b
h
2
A
=
a
+
b
Subtract
b
b
b
:
Finally, we subtract
b
b
b
from both sides to solve for
a
a
a
.
\newline
a
=
2
A
h
−
b
a = \frac{2A}{h} - b
a
=
h
2
A
−
b
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What kind of sequence is this?
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2, 10, 50, 250, \ldots
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Choices:Choices:
\newline
[A]arithmetic
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Classify the series.
∑
n
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\newline
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[C]both
\text{[C]both}
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Question
Find the first three partial sums of the series.
\newline
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Write your answers as integers or fractions in simplest form.
\newline
S
1
=
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S
1
=
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\newline
S
2
=
S_2 =
S
2
=
____
\newline
S
3
=
S_3 =
S
3
=
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Find the third partial sum of the series.
\newline
3
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9
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15
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21
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27
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33
+
⋯
3 + 9 + 15 + 21 + 27 + 33 + \cdots
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15
+
21
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33
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\newline
Write your answer as an integer or a fraction in simplest form.
\newline
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3
=
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=
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Find the first three partial sums of the series.
\newline
1
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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
=
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\newline
S
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=
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=
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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
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16
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+
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\newline
Choices:
\newline
[A]converge
\text{[A]converge}
[A]converge
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[B]diverge
\text{[B]diverge}
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