Find a general term aS1U1B1nS1U1B0 for the geometric sequence. -\[a _ { 1 } = - \frac { 1 } { 5 } , r = - 5\]

A) $a _ { n } = - \frac { 1 } { 5 } - \frac { 1 } { 5 } ( n - 1 )$ B) $a _ { n } = - \frac { 1 } { 5 } + \frac { 6 } { 25 } ( n - 1 )$ C) $a _ { n } = - \frac { 1 } { 5 } \cdot ( - 5 ) ^ { n - 1 }$ D) $a _ { n } = \left( - \frac { 1 } { 5 } \right) ^ { n - 1 } + \frac { 6 } { 25 }$ A) $a _ { n } = - \frac { 1 } { 5 } - \frac { 1 } { 5 } ( n - 1 )$ B) $a _ { n } = - \frac { 1 } { 5 } + \frac { 6 } { 25 } ( n - 1 )$ C) $a _ { n } = - \frac { 1 } { 5 } \cdot ( - 5 ) ^ { n - 1 }$ D) $a _ { n } = \left( - \frac { 1 } { 5 } \right) ^ { n - 1 } + \frac { 6 } { 25 }$

Exam 7: Arithmetic Sequence: Common Difference and First n Terms

Graph the ellipse. - $\frac { ( x + 2 ) ^ { 2 } } { 9 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$ $Graph the ellipse. - \frac { ( x + 2 ) ^ { 2 } } { 9 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$

(Multiple Choice)

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Question 401

Write an equation for the hyperbola. -foci at $( 10 - \sqrt { 53 } , 7 ) , ( 10 + \sqrt { 53 } , 7 ) ; e = \frac { \sqrt { 53 } } { 7 }$

(Multiple Choice)

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Question 402

Find the sum of the first 116 positive multiples of 5.

(Multiple Choice)

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Question 403

Match the equation of a hyperbola with its description. - $\frac { ( y - 3 ) ^ { 2 } } { 36 } - \frac { ( x - 1 ) ^ { 2 } } { 64 } = 1$

(Multiple Choice)

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Question 404

Find a general term a_n for the geometric sequence. - $a _ { 1 } = - \frac { 1 } { 5 } , r = - 5$

(Multiple Choice)

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Question 405

A radio telescope has a parabolic surface. If it is 1 m deep and 20 m wide, how far is the focus from the vertex?

(Multiple Choice)

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Question 406

$\text { Suppose that } \mathrm { C } = 0 \text { in the equation } \mathrm { Ax } { } ^ { 2 } + \mathrm { Bx } + \mathrm { Cy } { } ^ { 2 } + \mathrm { Dy } + \mathrm { E } = 0 \text {. What kind of graph does this equation have? }$

(Short Answer)

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Question 407

Find all natural number values for n for which the given statement is false. - $\mathrm { n } ! > 10 \mathrm { n }$

(Multiple Choice)

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Question 408

Graph the equation. Give the domain and range. Identify whether the equation is a function. - $\frac { y } { 7 } = \sqrt { 1 + \frac { x ^ { 2 } } { 36 } }$ $Graph the equation. Give the domain and range. Identify whether the equation is a function. - \frac { y } { 7 } = \sqrt { 1 + \frac { x ^ { 2 } } { 36 } }$

(Multiple Choice)

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Question 409

Find a formula for the nth term of the arithmetic sequence shown in the graph. -

(Multiple Choice)

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Question 410

Provide an appropriate response. -For 6, x, 12 to be an arithmetic sequence, x must be:

(Multiple Choice)

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Question 411

List the elements in the sample space of the experiment. -An 8-sided die is rolled. The sides contain the numbers 1, 2, 3, 4, 5, 6, 7, 8. List the sample space of rolling one die.

(Multiple Choice)

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Question 412

A signal is made by placing 3 flags, one above the other, on a flag pole. If there are 8 different flags available, how many possible signals can be flown?

(Multiple Choice)

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Question 413

Find the eccentricity $e$ of the ellipse. - $x ^ { 2 } + 25 y ^ { 2 } = 25$

(Multiple Choice)

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Question 414

How many ways can a class president, a class secretary, and a class treasurer be chosen from a group of 8 candidates?

(Multiple Choice)

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Question 415

Find the sum of the first n terms of the following arithmetic sequence. - $91,174,257 , \ldots ; \mathrm { n } = 10$

(Multiple Choice)

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Question 416

Write an equation for the parabola with vertex at the origin. -Focus (5, 0)

(Multiple Choice)

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Question 417

Provide an appropriate response. -Explain how to use the binomial theorem to expand ( $( 3 a - 7 b ) ^ { n }$

(Essay)

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Question 418

Evaluate the expression. - ${ } _ { 13 } \mathrm { C } _ { 7 }$

(Multiple Choice)

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Question 419

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or diverges. - $a _ { n } = \left( \frac { 1 } { 91 } + n \right) ^ { 1 / n }$

(Multiple Choice)

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Question 420

Graph the ellipse. - $\frac { ( x + 2 ) ^ { 2 } } { 9 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$ $Graph the ellipse. - \frac { ( x + 2 ) ^ { 2 } } { 9 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$

Write an equation for the hyperbola. -foci at $( 10 - \sqrt { 53 } , 7 ) , ( 10 + \sqrt { 53 } , 7 ) ; e = \frac { \sqrt { 53 } } { 7 }$

Find the sum of the first 116 positive multiples of 5.

Match the equation of a hyperbola with its description. - $\frac { ( y - 3 ) ^ { 2 } } { 36 } - \frac { ( x - 1 ) ^ { 2 } } { 64 } = 1$

Find a general term a_n for the geometric sequence. - $a _ { 1 } = - \frac { 1 } { 5 } , r = - 5$

A radio telescope has a parabolic surface. If it is 1 m deep and 20 m wide, how far is the focus from the vertex?

$\text { Suppose that } \mathrm { C } = 0 \text { in the equation } \mathrm { Ax } { } ^ { 2 } + \mathrm { Bx } + \mathrm { Cy } { } ^ { 2 } + \mathrm { Dy } + \mathrm { E } = 0 \text {. What kind of graph does this equation have? }$

Find all natural number values for n for which the given statement is false. - $\mathrm { n } ! > 10 \mathrm { n }$

Find a formula for the nth term of the arithmetic sequence shown in the graph. -

Provide an appropriate response. -For 6, x, 12 to be an arithmetic sequence, x must be:

List the elements in the sample space of the experiment. -An 8-sided die is rolled. The sides contain the numbers 1, 2, 3, 4, 5, 6, 7, 8. List the sample space of rolling one die.

A signal is made by placing 3 flags, one above the other, on a flag pole. If there are 8 different flags available, how many possible signals can be flown?

Find the eccentricity $e$ of the ellipse. - $x ^ { 2 } + 25 y ^ { 2 } = 25$

How many ways can a class president, a class secretary, and a class treasurer be chosen from a group of 8 candidates?

Find the sum of the first n terms of the following arithmetic sequence. - $91,174,257 , \ldots ; \mathrm { n } = 10$

Write an equation for the parabola with vertex at the origin. -Focus (5, 0)

Provide an appropriate response. -Explain how to use the binomial theorem to expand ( $( 3 a - 7 b ) ^ { n }$

Evaluate the expression. - ${ } _ { 13 } \mathrm { C } _ { 7 }$

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or diverges. - $a _ { n } = \left( \frac { 1 } { 91 } + n \right) ^ { 1 / n }$

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Filters

Exam 7: Arithmetic Sequence: Common Difference and First n Terms

Graph the ellipse. - (x+2)29+(y−1)24=1\frac { ( x + 2 ) ^ { 2 } } { 9 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 19(x+2)2​+4(y−1)2​=1

Write an equation for the hyperbola. -foci at (10−53,7),(10+53,7);e=537( 10 - \sqrt { 53 } , 7 ) , ( 10 + \sqrt { 53 } , 7 ) ; e = \frac { \sqrt { 53 } } { 7 }(10−53​,7),(10+53​,7);e=753​​

Find the sum of the first 116 positive multiples of 5.

Match the equation of a hyperbola with its description. - (y−3)236−(x−1)264=1\frac { ( y - 3 ) ^ { 2 } } { 36 } - \frac { ( x - 1 ) ^ { 2 } } { 64 } = 136(y−3)2​−64(x−1)2​=1

Find a general term an for the geometric sequence. - a1=−15,r=−5a _ { 1 } = - \frac { 1 } { 5 } , r = - 5a1​=−51​,r=−5

A radio telescope has a parabolic surface. If it is 1 m deep and 20 m wide, how far is the focus from the vertex?

Find all natural number values for n for which the given statement is false. - n!>10n\mathrm { n } ! > 10 \mathrm { n }n!>10n

Graph the equation. Give the domain and range. Identify whether the equation is a function. - y7=1+x236\frac { y } { 7 } = \sqrt { 1 + \frac { x ^ { 2 } } { 36 } }7y​=1+36x2​​

Find a formula for the nth term of the arithmetic sequence shown in the graph. -

Provide an appropriate response. -For 6, x, 12 to be an arithmetic sequence, x must be:

List the elements in the sample space of the experiment. -An 8-sided die is rolled. The sides contain the numbers 1, 2, 3, 4, 5, 6, 7, 8. List the sample space of rolling one die.

A signal is made by placing 3 flags, one above the other, on a flag pole. If there are 8 different flags available, how many possible signals can be flown?

Find the eccentricity e e e of the ellipse. - x2+25y2=25x ^ { 2 } + 25 y ^ { 2 } = 25x2+25y2=25

How many ways can a class president, a class secretary, and a class treasurer be chosen from a group of 8 candidates?

Find the sum of the first n terms of the following arithmetic sequence. - 91,174,257,…;n=1091,174,257 , \ldots ; \mathrm { n } = 1091,174,257,…;n=10

Write an equation for the parabola with vertex at the origin. -Focus (5, 0)

Provide an appropriate response. -Explain how to use the binomial theorem to expand ( (3a−7b)n( 3 a - 7 b ) ^ { n }(3a−7b)n

Evaluate the expression. - 13C7{ } _ { 13 } \mathrm { C } _ { 7 }13​C7​

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or diverges. - an=(191+n)1/na _ { n } = \left( \frac { 1 } { 91 } + n \right) ^ { 1 / n }an​=(911​+n)1/n

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Filters

Graph the ellipse. - $\frac { ( x + 2 ) ^ { 2 } } { 9 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$ $Graph the ellipse. - \frac { ( x + 2 ) ^ { 2 } } { 9 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$

Write an equation for the hyperbola. -foci at $( 10 - \sqrt { 53 } , 7 ) , ( 10 + \sqrt { 53 } , 7 ) ; e = \frac { \sqrt { 53 } } { 7 }$

Match the equation of a hyperbola with its description. - $\frac { ( y - 3 ) ^ { 2 } } { 36 } - \frac { ( x - 1 ) ^ { 2 } } { 64 } = 1$

Find a general term a_n for the geometric sequence. - $a _ { 1 } = - \frac { 1 } { 5 } , r = - 5$

Find all natural number values for n for which the given statement is false. - $\mathrm { n } ! > 10 \mathrm { n }$

Find the eccentricity $e$ of the ellipse. - $x ^ { 2 } + 25 y ^ { 2 } = 25$

Find the sum of the first n terms of the following arithmetic sequence. - $91,174,257 , \ldots ; \mathrm { n } = 10$

Provide an appropriate response. -Explain how to use the binomial theorem to expand ( $( 3 a - 7 b ) ^ { n }$

Evaluate the expression. - ${ } _ { 13 } \mathrm { C } _ { 7 }$

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or diverges. - $a _ { n } = \left( \frac { 1 } { 91 } + n \right) ^ { 1 / n }$