Write the statements SS1U1B11S1U1B0, SS1U1B12S1U1B0, and SS1U1B13S1U1B0 and determine if each statement is true. -\[S _ { n } : 2 + 7 + 12 + \ldots + ( 5 n - 3 ) = \frac { n ( 5 n - 1 ) } { 2 }\]

\[\begin{array}{l} S _ { 1 } : 2 = \frac

Exam 9: Sequences and Series; Counting and Probability

Solve the problem. -A hot dog stand sells hot dogs with cheese, relish, chili, tomato, onion, mustard, or ketchup. How many different hot dogs can be concocted using any 3 of the extras?

(Multiple Choice)

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Question 161

Determine if the infinite geometric series converges or diverges. If the series converges, find its sum. - $4 + \frac { 4 } { 5 } + \frac { 4 } { 25 } + \frac { 4 } { 125 } + \ldots$

(Multiple Choice)

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Question 162

Solve the problem. -A job pays a salary of 27,000 the first year. During the next 9 years, the salary increases by 5% each year. What is the salary for the 10th year? What is the total salary over the 10-year period? (Round to the nearest cent.)

(Multiple Choice)

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Question 163

Write the first five terms of the geometric sequence with the given information. -The first term is 8 and the common ratio is $- \frac { 1 } { 4 }$ .

(Multiple Choice)

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Question 164

-A box contains 3 blue cards numbered 1 through 3, and 4 green cards numbered 1 through 4. State the number of elements in the sample space of picking a blue card followed by a green card.

(Multiple Choice)

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Question 165

Rewrite the series using summation notation. Use 1 as the lower limit of summation. - $- \frac { 1 } { 3 } + \frac { 1 } { 6 } - \frac { 1 } { 9 } + \ldots - \frac { 1 } { 21 }$

(Multiple Choice)

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Question 166

-A box contains 2 blue cards numbered 1 through 2, and 3 green cards numbered 1 through 3. State the number of elements in the sample space of picking a blue card followed by a green card.

(Multiple Choice)

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Question 167

Solve the problem. - $\frac { 1 } { 25 } ,$ what are the odds against an earthquake?

(Multiple Choice)

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Question 168

Write the first five terms of the geometric sequence with the given information. - $a _ { n } = - 2 a _ { n } - 1 ; a _ { 1 } = - 3$

(Multiple Choice)

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Question 169

Write the first four terms of the sequence. - $a _ { n } = \frac { 2 ^ { n } } { ( n + 2 ) ! }$

(Multiple Choice)

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Question 170

Provide an appropriate response. -Find the 7th term of the geometric sequence -1, 3, -9, . . . .

(Multiple Choice)

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Question 171

Find the general term of the arithmetic sequence then find the indicated term of the sequence. Assume that the domain of the sequence is all natural numbers. -Find $a _ { n }$ and $a _ { 18 }$ . $Find the general term of the arithmetic sequence then find the indicated term of the sequence. Assume that the domain of the sequence is all natural numbers. -Find a _ { n } and a _ { 18 } .$

(Multiple Choice)

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Question 172

Solve the problem. -A certain club initially has 100 members and membership increases by 5 members every month. If dues are $5/month, what is the total amount of dues collected during the first year?

(Multiple Choice)

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Question 173

Find the indicated sum. -19 + 24 + 29 + 34 + . . . + a60

(Multiple Choice)

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(30)

Question 174

Find the general term of the arithmetic sequence. - $\frac { 1 } { 6 } , \frac { 2 } { 3 } , \frac { 7 } { 6 } , \frac { 5 } { 3 } , \frac { 13 } { 6 } , \ldots$

(Multiple Choice)

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Question 175

Solve the problem. -In how many ways can 8 people be lined up?

(Multiple Choice)

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Question 176

Evaluate the binomial coefficient. - $\left( \begin{array} { l } 5 \\ 1 \end{array} \right)$

(Multiple Choice)

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Question 177

Solve the problem. -A person puts $20 into a bank account on January 1, $25 on February 1, $30 on March 1, and so forth. How much has the person put into the bank account by December 30?

(Multiple Choice)

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(33)

Question 178

Write the statements S₁, S₂, and S₃ and determine if each statement is true. - $S _ { n } : 2 + 7 + 12 + \ldots + ( 5 n - 3 ) = \frac { n ( 5 n - 1 ) } { 2 }$

(Essay)

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Question 179

The general term of a sequence is given. Find the indicated partial sum. - $a _ { n } = \frac { ( - 1 ) ^ { n - 1 } } { 7 n } ; S _ { 4 }$

(Multiple Choice)

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Question 180

Showing 161 - 180 of 255

Solve the problem. -A hot dog stand sells hot dogs with cheese, relish, chili, tomato, onion, mustard, or ketchup. How many different hot dogs can be concocted using any 3 of the extras?

Determine if the infinite geometric series converges or diverges. If the series converges, find its sum. - $4 + \frac { 4 } { 5 } + \frac { 4 } { 25 } + \frac { 4 } { 125 } + \ldots$

Solve the problem. -A job pays a salary of 27,000 the first year. During the next 9 years, the salary increases by 5% each year. What is the salary for the 10th year? What is the total salary over the 10-year period? (Round to the nearest cent.)

Write the first five terms of the geometric sequence with the given information. -The first term is 8 and the common ratio is $- \frac { 1 } { 4 }$ .

-A box contains 3 blue cards numbered 1 through 3, and 4 green cards numbered 1 through 4. State the number of elements in the sample space of picking a blue card followed by a green card.

Rewrite the series using summation notation. Use 1 as the lower limit of summation. - $- \frac { 1 } { 3 } + \frac { 1 } { 6 } - \frac { 1 } { 9 } + \ldots - \frac { 1 } { 21 }$

-A box contains 2 blue cards numbered 1 through 2, and 3 green cards numbered 1 through 3. State the number of elements in the sample space of picking a blue card followed by a green card.

Solve the problem. - $\frac { 1 } { 25 } ,$ what are the odds against an earthquake?

Write the first five terms of the geometric sequence with the given information. - $a _ { n } = - 2 a _ { n } - 1 ; a _ { 1 } = - 3$

Write the first four terms of the sequence. - $a _ { n } = \frac { 2 ^ { n } } { ( n + 2 ) ! }$

Provide an appropriate response. -Find the 7th term of the geometric sequence -1, 3, -9, . . . .

Solve the problem. -A certain club initially has 100 members and membership increases by 5 members every month. If dues are $5/month, what is the total amount of dues collected during the first year?

Find the indicated sum. -19 + 24 + 29 + 34 + . . . + a60

Find the general term of the arithmetic sequence. - $\frac { 1 } { 6 } , \frac { 2 } { 3 } , \frac { 7 } { 6 } , \frac { 5 } { 3 } , \frac { 13 } { 6 } , \ldots$

Solve the problem. -In how many ways can 8 people be lined up?

Evaluate the binomial coefficient. - $\left( \begin{array} { l } 5 \\ 1 \end{array} \right)$

Solve the problem. -A person puts $20 into a bank account on January 1, $25 on February 1, $30 on March 1, and so forth. How much has the person put into the bank account by December 30?

Write the statements S₁, S₂, and S₃ and determine if each statement is true. - $S _ { n } : 2 + 7 + 12 + \ldots + ( 5 n - 3 ) = \frac { n ( 5 n - 1 ) } { 2 }$

The general term of a sequence is given. Find the indicated partial sum. - $a _ { n } = \frac { ( - 1 ) ^ { n - 1 } } { 7 n } ; S _ { 4 }$

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

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Math Exercises: Sets, Intervals, Absolute Value, and Properties

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Exam 9: Sequences and Series; Counting and Probability

Solve the problem. -A hot dog stand sells hot dogs with cheese, relish, chili, tomato, onion, mustard, or ketchup. How many different hot dogs can be concocted using any 3 of the extras?

Determine if the infinite geometric series converges or diverges. If the series converges, find its sum. - 4+45+425+4125+…4 + \frac { 4 } { 5 } + \frac { 4 } { 25 } + \frac { 4 } { 125 } + \ldots4+54​+254​+1254​+…

Solve the problem. -A job pays a salary of 27,000 the first year. During the next 9 years, the salary increases by 5% each year. What is the salary for the 10th year? What is the total salary over the 10-year period? (Round to the nearest cent.)

Write the first five terms of the geometric sequence with the given information. -The first term is 8 and the common ratio is −14- \frac { 1 } { 4 }−41​ .

-A box contains 3 blue cards numbered 1 through 3, and 4 green cards numbered 1 through 4. State the number of elements in the sample space of picking a blue card followed by a green card.

Rewrite the series using summation notation. Use 1 as the lower limit of summation. - −13+16−19+…−121- \frac { 1 } { 3 } + \frac { 1 } { 6 } - \frac { 1 } { 9 } + \ldots - \frac { 1 } { 21 }−31​+61​−91​+…−211​

-A box contains 2 blue cards numbered 1 through 2, and 3 green cards numbered 1 through 3. State the number of elements in the sample space of picking a blue card followed by a green card.

Solve the problem. - 125,\frac { 1 } { 25 } ,251​, what are the odds against an earthquake?

Write the first five terms of the geometric sequence with the given information. - an=−2an−1;a1=−3a _ { n } = - 2 a _ { n } - 1 ; a _ { 1 } = - 3an​=−2an​−1;a1​=−3

Write the first four terms of the sequence. - an=2n(n+2)!a _ { n } = \frac { 2 ^ { n } } { ( n + 2 ) ! }an​=(n+2)!2n​

Provide an appropriate response. -Find the 7th term of the geometric sequence -1, 3, -9, . . . .

Find the general term of the arithmetic sequence then find the indicated term of the sequence. Assume that the domain of the sequence is all natural numbers. -Find ana _ { n }an​ and a18a _ { 18 }a18​ .

Solve the problem. -A certain club initially has 100 members and membership increases by 5 members every month. If dues are $5/month, what is the total amount of dues collected during the first year?

Find the indicated sum. -19 + 24 + 29 + 34 + . . . + a60

Find the general term of the arithmetic sequence. - 16,23,76,53,136,…\frac { 1 } { 6 } , \frac { 2 } { 3 } , \frac { 7 } { 6 } , \frac { 5 } { 3 } , \frac { 13 } { 6 } , \ldots61​,32​,67​,35​,613​,…

Solve the problem. -In how many ways can 8 people be lined up?

Evaluate the binomial coefficient. - (51)\left( \begin{array} { l } 5 \\ 1 \end{array} \right)(51​)

Solve the problem. -A person puts $20 into a bank account on January 1, $25 on February 1, $30 on March 1, and so forth. How much has the person put into the bank account by December 30?

Write the statements S1, S2, and S3 and determine if each statement is true. - Sn:2+7+12+…+(5n−3)=n(5n−1)2S _ { n } : 2 + 7 + 12 + \ldots + ( 5 n - 3 ) = \frac { n ( 5 n - 1 ) } { 2 }Sn​:2+7+12+…+(5n−3)=2n(5n−1)​

The general term of a sequence is given. Find the indicated partial sum. - an=(−1)n−17n;S4a _ { n } = \frac { ( - 1 ) ^ { n - 1 } } { 7 n } ; S _ { 4 }an​=7n(−1)n−1​;S4​

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Determine if the infinite geometric series converges or diverges. If the series converges, find its sum. - $4 + \frac { 4 } { 5 } + \frac { 4 } { 25 } + \frac { 4 } { 125 } + \ldots$

Write the first five terms of the geometric sequence with the given information. -The first term is 8 and the common ratio is $- \frac { 1 } { 4 }$ .

Rewrite the series using summation notation. Use 1 as the lower limit of summation. - $- \frac { 1 } { 3 } + \frac { 1 } { 6 } - \frac { 1 } { 9 } + \ldots - \frac { 1 } { 21 }$

Solve the problem. - $\frac { 1 } { 25 } ,$ what are the odds against an earthquake?

Write the first five terms of the geometric sequence with the given information. - $a _ { n } = - 2 a _ { n } - 1 ; a _ { 1 } = - 3$

Write the first four terms of the sequence. - $a _ { n } = \frac { 2 ^ { n } } { ( n + 2 ) ! }$

Find the general term of the arithmetic sequence. - $\frac { 1 } { 6 } , \frac { 2 } { 3 } , \frac { 7 } { 6 } , \frac { 5 } { 3 } , \frac { 13 } { 6 } , \ldots$

Evaluate the binomial coefficient. - $\left( \begin{array} { l } 5 \\ 1 \end{array} \right)$

Write the statements S₁, S₂, and S₃ and determine if each statement is true. - $S _ { n } : 2 + 7 + 12 + \ldots + ( 5 n - 3 ) = \frac { n ( 5 n - 1 ) } { 2 }$

The general term of a sequence is given. Find the indicated partial sum. - $a _ { n } = \frac { ( - 1 ) ^ { n - 1 } } { 7 n } ; S _ { 4 }$