The general term of a sequence is given. Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. -The following table shows a country's population from 1995 to 1998: \[\begin{array} { l | l l l } \text { Year } & 1995199619971998 \\ \hline \text { Population in millions } & 12.2012 .8113 .4514 .12 \end{array}\] Divide the population for each year by the population in the preceding year. Use this ratio to write the general term of the geometric sequence describing the country's population growth n years after 1994. Then estimate the country's population, in millions, in 2005.

A) $\mathrm { a } _ { \mathrm { n } } = 12.20 ( 1.05 ) ^ { \mathrm { n } - 1 ; 19.87 \text { million } }$ B) $a _ { n } = 12.20 ( 1.05 ) ^ { n - 1 ; } 20.87$ million C) $\mathrm { a } _ { \mathrm { n } } = 12.20 ( 1.04 ) ^ { \mathrm { n } - 1 } ; 24$ million D) $a _ { n } = 12.20 ( 1.04 ) ^ { n - 1 ; 22.43 \text { million } }$ A) $\mathrm { a } _ { \mathrm { n } } = 12.20 ( 1.05 ) ^ { \mathrm { n } - 1 ; 19.87 \text { million } }$ B) $a _ { n } = 12.20 ( 1.05 ) ^ { n - 1 ; } 20.87$ million C) $\mathrm { a } _ { \mathrm { n } } = 12.20 ( 1.04 ) ^ { \mathrm { n } - 1 } ; 24$ million D) $a _ { n } = 12.20 ( 1.04 ) ^ { n - 1 ; 22.43 \text { million } }$

Exam 11: Sequences, Induction, and Probability

Use the Formula for the Sum of the First n Terms of a Geometric Sequence -Find the sum of the first 11 terms of the geometric sequence: 5, 10, 20, 40, 80, . . . .

(Multiple Choice)

4.8/5

(29)

Question 81

Probability 1 Compute Empirical Probability -A traffic engineer is counting the number of vehicles by type that turn into a residential area. The table below shows the results of the counts during a four-hour period. What is the probability that the next vehicle passing is an SUV?

(Multiple Choice)

4.9/5

(31)

Question 82

Use the Formula for the Sum of the First n Terms of an Arithmetic Sequence -Find the sum of the first 40 terms of the arithmetic sequence: 18, 28, 38, 48, . . .

(Multiple Choice)

4.8/5

(27)

Question 83

Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence. -A job pays a salary of 30,000 the first year. During the next 7 years, the salary increases by 4% each year. What is the salary for the 8th year? What is the total salary over the 8-year period? (Round to the nearest cent.)

(Multiple Choice)

4.8/5

(33)

Question 84

Use the Formula for the Sum of the First n Terms of an Arithmetic Sequence -Find the sum of the odd integers between 38 and 70.

(Multiple Choice)

4.7/5

(33)

Question 85

Compute Theoretical Probability -Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the die will be 3 ?

(Multiple Choice)

4.9/5

(38)

Question 86

Write the first four terms of the sequence whose general term is given. - $a _ { n } = \frac { 4 } { n ^ { 2 } }$

(Multiple Choice)

4.8/5

(37)

Question 87

Compute Theoretical Probability -A bag contains 5 red marbles, 6 blue marbles, and 2 green marbles. What is the probability of choosing a blue marble when one marble is drawn?

(Multiple Choice)

4.9/5

(43)

Question 88

Compute Theoretical Probability -A bag contains 17 balls numbered 1 through $17 .$ What is the probability of selecting a ball that has an even number when one ball is drawn from the bag?

(Multiple Choice)

4.7/5

(38)

Question 89

The general term of a sequence is given. Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. -The following table shows a country's population from 1995 to 1998: Year 1995199619971998 Population in millions 12.2012.8113.4514.12 Divide the population for each year by the population in the preceding year. Use this ratio to write the general term of the geometric sequence describing the country's population growth n years after 1994. Then estimate the country's population, in millions, in 2005.

(Multiple Choice)

4.9/5

(44)

Question 90

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. - $\frac { 1 } { 3 } + \frac { 1 } { 2 } + \frac { 3 } { 5 } + \ldots + \frac { 7 } { 8 }$

(Multiple Choice)

4.9/5

(32)

Question 91

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. - $\sum _ { i = 1 } ^ { 44 } ( 5 i - 3 )$

(Multiple Choice)

4.8/5

(40)

Question 92

Use Summation Notation - $\sum _ { i = 2 } ^ { 5 } 11$

(Multiple Choice)

4.9/5

(42)

Question 93

Use the Formula for the Sum of the First n Terms of a Geometric Sequence -Find the sum of the first 10 terms of the geometric sequence: 7, -14, 28, -56, 112, . . . .

(Multiple Choice)

4.8/5

(31)

Question 94

Use the Combinations Formula -11C3

(Multiple Choice)

4.7/5

(44)

Question 95

Probability 1 Compute Empirical Probability -In 1999 the stock market took big swings up and down. A survey of 991 adult investors asked how often they tracked their portfolio. The table shows the investor responses. What is the probability that an adult investor tracks his or her portfolio daily?

(Multiple Choice)

4.8/5

(38)

Question 96

Write the first four terms of the sequence whose general term is given. -A deposit of $\$ 11,000$ is made in an account that earns $5.6 \%$ interest compounded quarterly. The balance in the account after $n$ quarters is given by the sequence $a _ { n } = 11,000 \left( 1 + \frac { 0.056 } { 4 } \right) ^ { n } , n = 1,2,3 , \ldots$ Find the balance in the account after 4 years.

(Multiple Choice)

4.8/5

(27)

Question 97

Use Factorial Notation - $\frac { ( n + 6 ) ! } { n + 6 }$

(Multiple Choice)

4.9/5

(42)

Question 98

Arithmetic Sequences Find the Common Difference for an Arithmetic Sequence - $624,616,608,600 , \ldots$

(Multiple Choice)

4.8/5

(42)

Question 99

Use the Formula for the General Term of a Geometric Sequence -Find $a _ { 8 }$ when $a _ { 1 } = 3 , r = - 2$ .

(Multiple Choice)

4.8/5

(35)

Question 100

Showing 81 - 100 of 304

Use the Formula for the Sum of the First n Terms of a Geometric Sequence -Find the sum of the first 11 terms of the geometric sequence: 5, 10, 20, 40, 80, . . . .

Probability 1 Compute Empirical Probability -A traffic engineer is counting the number of vehicles by type that turn into a residential area. The table below shows the results of the counts during a four-hour period. What is the probability that the next vehicle passing is an SUV?

Use the Formula for the Sum of the First n Terms of an Arithmetic Sequence -Find the sum of the first 40 terms of the arithmetic sequence: 18, 28, 38, 48, . . .

Use the Formula for the Sum of the First n Terms of an Arithmetic Sequence -Find the sum of the odd integers between 38 and 70.

Compute Theoretical Probability -Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the die will be 3 ?

Write the first four terms of the sequence whose general term is given. - $a _ { n } = \frac { 4 } { n ^ { 2 } }$

Compute Theoretical Probability -A bag contains 5 red marbles, 6 blue marbles, and 2 green marbles. What is the probability of choosing a blue marble when one marble is drawn?

Compute Theoretical Probability -A bag contains 17 balls numbered 1 through $17 .$ What is the probability of selecting a ball that has an even number when one ball is drawn from the bag?

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. - $\frac { 1 } { 3 } + \frac { 1 } { 2 } + \frac { 3 } { 5 } + \ldots + \frac { 7 } { 8 }$

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. - $\sum _ { i = 1 } ^ { 44 } ( 5 i - 3 )$

Use Summation Notation - $\sum _ { i = 2 } ^ { 5 } 11$

Use the Formula for the Sum of the First n Terms of a Geometric Sequence -Find the sum of the first 10 terms of the geometric sequence: 7, -14, 28, -56, 112, . . . .

Use the Combinations Formula -11C3

Probability 1 Compute Empirical Probability -In 1999 the stock market took big swings up and down. A survey of 991 adult investors asked how often they tracked their portfolio. The table shows the investor responses. What is the probability that an adult investor tracks his or her portfolio daily?

Use Factorial Notation - $\frac { ( n + 6 ) ! } { n + 6 }$

Arithmetic Sequences Find the Common Difference for an Arithmetic Sequence - $624,616,608,600 , \ldots$

Use the Formula for the General Term of a Geometric Sequence -Find $a _ { 8 }$ when $a _ { 1 } = 3 , r = - 2$ .

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections and Analytic Geometry

Prerequisites: Fundamental Concepts of Algebra

Filters

Exam 11: Sequences, Induction, and Probability

Use the Formula for the Sum of the First n Terms of a Geometric Sequence -Find the sum of the first 11 terms of the geometric sequence: 5, 10, 20, 40, 80, . . . .

Probability 1 Compute Empirical Probability -A traffic engineer is counting the number of vehicles by type that turn into a residential area. The table below shows the results of the counts during a four-hour period. What is the probability that the next vehicle passing is an SUV?

Use the Formula for the Sum of the First n Terms of an Arithmetic Sequence -Find the sum of the first 40 terms of the arithmetic sequence: 18, 28, 38, 48, . . .

Use the Formula for the Sum of the First n Terms of an Arithmetic Sequence -Find the sum of the odd integers between 38 and 70.

Compute Theoretical Probability -Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the die will be 3 ?

Write the first four terms of the sequence whose general term is given. - an=4n2a _ { n } = \frac { 4 } { n ^ { 2 } }an​=n24​

Compute Theoretical Probability -A bag contains 5 red marbles, 6 blue marbles, and 2 green marbles. What is the probability of choosing a blue marble when one marble is drawn?

Compute Theoretical Probability -A bag contains 17 balls numbered 1 through 17.17 .17. What is the probability of selecting a ball that has an even number when one ball is drawn from the bag?

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. - 13+12+35+…+78\frac { 1 } { 3 } + \frac { 1 } { 2 } + \frac { 3 } { 5 } + \ldots + \frac { 7 } { 8 }31​+21​+53​+…+87​

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. - ∑i=144(5i−3)\sum _ { i = 1 } ^ { 44 } ( 5 i - 3 )∑i=144​(5i−3)

Use Summation Notation - ∑i=2511\sum _ { i = 2 } ^ { 5 } 11∑i=25​11

Use the Formula for the Sum of the First n Terms of a Geometric Sequence -Find the sum of the first 10 terms of the geometric sequence: 7, -14, 28, -56, 112, . . . .

Use the Combinations Formula -11C3

Probability 1 Compute Empirical Probability -In 1999 the stock market took big swings up and down. A survey of 991 adult investors asked how often they tracked their portfolio. The table shows the investor responses. What is the probability that an adult investor tracks his or her portfolio daily?

Use Factorial Notation - (n+6)!n+6\frac { ( n + 6 ) ! } { n + 6 }n+6(n+6)!​

Arithmetic Sequences Find the Common Difference for an Arithmetic Sequence - 624,616,608,600,…624,616,608,600 , \ldots624,616,608,600,…

Use the Formula for the General Term of a Geometric Sequence -Find a8a _ { 8 }a8​ when a1=3,r=−2a _ { 1 } = 3 , r = - 2a1​=3,r=−2 .

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections and Analytic Geometry

Prerequisites: Fundamental Concepts of Algebra

Filters

Write the first four terms of the sequence whose general term is given. - $a _ { n } = \frac { 4 } { n ^ { 2 } }$

Compute Theoretical Probability -A bag contains 17 balls numbered 1 through $17 .$ What is the probability of selecting a ball that has an even number when one ball is drawn from the bag?

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. - $\frac { 1 } { 3 } + \frac { 1 } { 2 } + \frac { 3 } { 5 } + \ldots + \frac { 7 } { 8 }$

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. - $\sum _ { i = 1 } ^ { 44 } ( 5 i - 3 )$

Use Summation Notation - $\sum _ { i = 2 } ^ { 5 } 11$

Use Factorial Notation - $\frac { ( n + 6 ) ! } { n + 6 }$

Arithmetic Sequences Find the Common Difference for an Arithmetic Sequence - $624,616,608,600 , \ldots$

Use the Formula for the General Term of a Geometric Sequence -Find $a _ { 8 }$ when $a _ { 1 } = 3 , r = - 2$ .