Question 1

Find the nth term and the indicated term of the arithmetic sequence whose initial term, a, and common difference,
d, are given.
-

Accepted Answer

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

Question 2

Solve.
-A small business owner made $40,000 the first year he owned his store and made an additional 6% overthe previous year in each subsequent year. Find how much he made during his fourth year of business.Find his total earnings during the first four years. (Round to the nearest cent, if necessary.)

Accepted Answer

A) $47,640.64; $174,984.64 
B) $8.64; $42,552.64 
C) $163,840.00; $370,240.00 
D) $262,144.00; $632,384.00 
A) $47,640.64; $174,984.64 
B) $8.64; $42,552.64 
C) $163,840.00; $370,240.00 
D) $262,144.00; $632,384.00

Question 3

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given.
-

Accepted Answer

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

Question 4

Write the word or phrase that best completes each statement or answers the question.
-Joytown has a present population of 40,000 and the population is increasing by 2.5% each year. How longwill it take for the population to double? Round your answer to the nearest year.

Accepted Answer

A) 28 years 
B) 40 years 
C) 29 years 
D) 41 years 
A) 28 years 
B) 40 years 
C) 29 years 
D) 41 years

Question 5

Find the sum.
-

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

Solve.
-A bicycle wheel rotates 400 times in a minute as long as the rider is pedaling. If the rider stops pedaling,the wheel starts to slow down. Each minute it will rotate only   as many times as in the precedingminute. How many times will the wheel rotate in the 5th minute after the riderʹs feet leave the pedals?Round your answer to the nearest unit.

Accepted Answer

A) 95 times 
B) 127 times 
C) 0 times 
D) 2 times 
A) 95 times 
B) 127 times 
C) 0 times 
D) 2 times

Question 8

Solve.
-For the geometric sequence 64, 16, 4, 1, ... , find a

Accepted Answer

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

Question 9

Determine whether the sequence is arithmetic.
-5, -15, 45, -135, 405, ...

Accepted Answer

A) Arithmetic 
B) Not arithmetic 
A) Arithmetic 
B) Not arithmetic

Question 10

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum.
-

Accepted Answer

A) Converges; - 20 
B) Converges; 10 
C) Converges;   
D) Diverges 
A) Converges; - 20 
B) Converges; 10 
C) Converges;   
D) Diverges

Question 11

Evaluate the expression.
-

Accepted Answer

A) 28 
B) 8 
C) 0 
D) 1 
A) 28 
B) 8 
C) 0 
D) 1

Question 12

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.
-9, 11, 14,18, ...

Accepted Answer

A) Geometric; r = 9 
B) Arithmetic; d = 9 
C) Geometric; r = 81 
D) Neither 
A) Geometric; r = 9 
B) Arithmetic; d = 9 
C) Geometric; r = 81 
D) Neither

Question 13

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given.
-

Accepted Answer

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

Question 14

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.
-Show that the formula2 + 4 + 6 + 8 + ... + 2n =   + n + 3obeys Condition II of the Principle of Mathematical Induction. That is, show that if the formula is true for sonatural number k, it is also true for the next natural number k + 1. Then show that the formula is false forn = 1.

Accepted Answer

Assume the statement is true for some na

Question 15

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary.
-6 - 18 + 54 - 162 + 486 - ... +

Accepted Answer

A) 265,722 
B) 265,720 
C) 265,729 
D) 265,716 
A) 265,722 
B) 265,720 
C) 265,729 
D) 265,716

Question 16

Write the word or phrase that best completes each statement or answers the question.
-Christine contributes $100 each month to her 401(k). To the nearest dollar, what will be the value ofChristineʹs 401(k)in 20 years if the per annum rate of return is assumed to be 10% compounded monthly.

Accepted Answer

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

Question 17

Determine whether the sequence is arithmetic.
-4, 12, 36, 108, 972, ...

Accepted Answer

A) Arithmetic 
B) Not arithmetic 
A) Arithmetic 
B) Not arithmetic

Question 18

Expand the expression using the Binomial Theorem.
-

Accepted Answer

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

Question 19

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum.
-

Accepted Answer

A) Converges;   
B) Converges; 5 
C) Converges;   
D) Diverges 
A) Converges;   
B) Converges; 5 
C) Converges;   
D) Diverges

Question 20

Evaluate the factorial expression.
-

Accepted Answer

A) 21 
B) 7 
C) 0 
D) 1 
A) 21 
B) 7 
C) 0 
D) 1

Find the nth term and the indicated term of the arithmetic sequence whose initial term, a, and common difference, d, are given. -

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. -

Write the word or phrase that best completes each statement or answers the question. -Joytown has a present population of 40,000 and the population is increasing by 2.5% each year. How longwill it take for the population to double? Round your answer to the nearest year.

Find the sum. -

Expand the expression using the Binomial Theorem. -

Solve. -For the geometric sequence 64, 16, 4, 1, ... , find a

Determine whether the sequence is arithmetic. -5, -15, 45, -135, 405, ...

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. -

Evaluate the expression. -

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. -9, 11, 14,18, ...

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. -

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. -6 - 18 + 54 - 162 + 486 - ... +

Write the word or phrase that best completes each statement or answers the question. -Christine contributes $100 each month to her 401(k). To the nearest dollar, what will be the value ofChristineʹs 401(k)in 20 years if the per annum rate of return is assumed to be 10% compounded monthly.

Determine whether the sequence is arithmetic. -4, 12, 36, 108, 972, ...

Expand the expression using the Binomial Theorem. -

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. -

Evaluate the factorial expression. -

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Exam 9: Sequences; Induction; the Binomial Theorem

Find the nth term and the indicated term of the arithmetic sequence whose initial term, a, and common difference, d, are given. -

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. -

Write the word or phrase that best completes each statement or answers the question. -Joytown has a present population of 40,000 and the population is increasing by 2.5% each year. How longwill it take for the population to double? Round your answer to the nearest year.

Find the sum. -

Expand the expression using the Binomial Theorem. -

Solve. -For the geometric sequence 64, 16, 4, 1, ... , find a

Determine whether the sequence is arithmetic. -5, -15, 45, -135, 405, ...

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. -

Evaluate the expression. -

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. -9, 11, 14,18, ...

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. -

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. -6 - 18 + 54 - 162 + 486 - ... +

Write the word or phrase that best completes each statement or answers the question. -Christine contributes $100 each month to her 401(k). To the nearest dollar, what will be the value ofChristineʹs 401(k)in 20 years if the per annum rate of return is assumed to be 10% compounded monthly.

Determine whether the sequence is arithmetic. -4, 12, 36, 108, 972, ...

Expand the expression using the Binomial Theorem. -

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. -

Evaluate the factorial expression. -

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