Question 1

Find the sum of the sequence.
-

Accepted Answer

A) 384 
B) 53 
C) 272 
D) 400 
A) 384 
B) 53 
C) 272 
D) 400

Question 2

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.
-3 - 1n

Accepted Answer

A) Arithmetic; d = - 1 
B) Geometric; r = - 1 
C) Arithmetic; d =3 
D) Neither 
A) Arithmetic; d = - 1 
B) Geometric; r = - 1 
C) Arithmetic; d =3 
D) Neither

Question 3

Solve.
-A ball is dropped from a height of 25 feet. Each time it strikes the ground, it bounces up to 0.7 of theprevious height. The total distance the ball has traveled before the second bounce is 25 + 2(25 ∙ 0.7)feet,and the total distance the ball has traveled before bounce n + 1 is   Use facts about infinite geometric series to calculate the total distance the ball has traveled by the time it hasstopped bouncing.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 4

Use the Binomial Theorem to find the indicated coefficient or term.
-The coefficient of x in the expansion of

Accepted Answer

A) 540 
B) 450 
C) 36 
D) 1,080 
A) 540 
B) 450 
C) 36 
D) 1,080

Question 5

Use the Binomial Theorem to find the indicated coefficient or term.
-The 5th term in the expansion of (

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 6

Expand the expression using the Binomial Theorem.
-

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 7

Find the sum.
-

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 8

A geometric sequence is given. Find the common ratio and write out the first four terms.
-

Accepted Answer

A)    
B)    
C) r   
D)    
A)    
B)    
C) r   
D)

Question 9

The sequence is defined recursively. Write the first four terms.
-

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 10

Solve.
-To save for retirement, you decide to deposit $2,500 into an IRA at the end of each year for the next 30years. If the interest rate is 7% per year compounded annually, find the value of the IRA after 30 years.(Round to the nearest dollar.)

Accepted Answer

A) $236,152 
B) $16,531 
C) $218,366 
D) $4,691,339 
A) $236,152 
B) $16,531 
C) $218,366 
D) $4,691,339

Question 11

Find the indicated term of the geometric sequence.
-7th term of 0.2, 0.02, 0.002, . . .

Accepted Answer

A) 0.0000002 
B) 0.00000002 
C) 0.000002 
D) 0 
A) 0.0000002 
B) 0.00000002 
C) 0.000002 
D) 0

Question 12

Solve.
-A ping-pong ball is dropped from a height of 9 ft and always rebounds   of the distance fallen. Find thetotal sum of the rebound heights of the ball.

Accepted Answer

A) 4.5 ft 
B) 13.5 ft 
C) 6 ft 
D) 3 ft 
A) 4.5 ft 
B) 13.5 ft 
C) 6 ft 
D) 3 ft

Question 13

Find the sum.
-2 + 4 + 6 + ... + 1,298

Accepted Answer

A) 421,850 
B) 421,201 
C) 420,552 
D) 422,500 
A) 421,850 
B) 421,201 
C) 420,552 
D) 422,500

Question 14

Evaluate the expression.
-

Accepted Answer

A) 20 
B) 40 
C) 120 
D) 10 
A) 20 
B) 40 
C) 120 
D) 10

Question 15

Expand the expression using the Binomial Theorem.
-

Accepted Answer

A)    
B)    
C) 1   
D)    
A)    
B)    
C) 1   
D)

Question 16

The sequence is defined recursively. Write the first four terms.
-

Accepted Answer

A)    
B) a   
C)    
D)    
A)    
B) a   
C)    
D)

Question 17

Write the word or phrase that best completes each statement or answers the question.
-Lexington Reservoir has 300 million gallons of water. About 0.07% of the water is lost to evaporation everyweek. About 150,000 gallons of water enter the reservoir every week. The amount of water in the reservoirat the end of each week is given by the recursively defined sequence   Determine the amount of water in the reservoir at the beginning of the second week. That is, determine

Accepted Answer

The answer of Write the word or phrase that best...

Question 18

Find the indicated term of the sequence.
-The fifteenth term of the arithmetic sequence 26, 22, 18, ...

Accepted Answer

A) -30 
B) -34 
C) -56 
D) 82 
A) -30 
B) -34 
C) -56 
D) 82

Question 19

Write out the first five terms of the sequence.
-

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 20

Mathematical Induction
1 Prove Statements Using Mathematical Induction
 Write the word or phrase that best completes each statement or answers the question.
Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.
-

Accepted Answer

First we show that the statement is true

Find the sum of the sequence. -

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. -3 - 1n

Use the Binomial Theorem to find the indicated coefficient or term. -The coefficient of x in the expansion of

Use the Binomial Theorem to find the indicated coefficient or term. -The 5th term in the expansion of (

Expand the expression using the Binomial Theorem. -

Find the sum. -

A geometric sequence is given. Find the common ratio and write out the first four terms. -

The sequence is defined recursively. Write the first four terms. -

Solve. -To save for retirement, you decide to deposit $2,500 into an IRA at the end of each year for the next 30years. If the interest rate is 7% per year compounded annually, find the value of the IRA after 30 years.(Round to the nearest dollar.)

Find the indicated term of the geometric sequence. -7th term of 0.2, 0.02, 0.002, . . .

Solve. -A ping-pong ball is dropped from a height of 9 ft and always rebounds of the distance fallen. Find thetotal sum of the rebound heights of the ball.

Find the sum. -2 + 4 + 6 + ... + 1,298

Evaluate the expression. -

Expand the expression using the Binomial Theorem. -

The sequence is defined recursively. Write the first four terms. -

Find the indicated term of the sequence. -The fifteenth term of the arithmetic sequence 26, 22, 18, ...

Write out the first five terms of the sequence. -

Mathematical Induction 1 Prove Statements Using Mathematical Induction Write the word or phrase that best completes each statement or answers the question. Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n. -

Equations and Inequalities

Graphs

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Geometry

Systems of Equations and Inequalities

Counting and Probability

Graphing Utilities

Filters

Exam 9: Sequences; Induction; the Binomial Theorem

Find the sum of the sequence. -

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. -3 - 1n

Use the Binomial Theorem to find the indicated coefficient or term. -The coefficient of x in the expansion of

Use the Binomial Theorem to find the indicated coefficient or term. -The 5th term in the expansion of (

Expand the expression using the Binomial Theorem. -

Find the sum. -

A geometric sequence is given. Find the common ratio and write out the first four terms. -

The sequence is defined recursively. Write the first four terms. -

Solve. -To save for retirement, you decide to deposit $2,500 into an IRA at the end of each year for the next 30years. If the interest rate is 7% per year compounded annually, find the value of the IRA after 30 years.(Round to the nearest dollar.)

Find the indicated term of the geometric sequence. -7th term of 0.2, 0.02, 0.002, . . .

Solve. -A ping-pong ball is dropped from a height of 9 ft and always rebounds of the distance fallen. Find thetotal sum of the rebound heights of the ball.

Find the sum. -2 + 4 + 6 + ... + 1,298

Evaluate the expression. -

Expand the expression using the Binomial Theorem. -

The sequence is defined recursively. Write the first four terms. -

Find the indicated term of the sequence. -The fifteenth term of the arithmetic sequence 26, 22, 18, ...

Write out the first five terms of the sequence. -

Mathematical Induction 1 Prove Statements Using Mathematical Induction Write the word or phrase that best completes each statement or answers the question. Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n. -

Equations and Inequalities

Graphs

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Geometry

Systems of Equations and Inequalities

Counting and Probability

Graphing Utilities

Filters