Question 1

Find the indicated term of the geometric sequence.
-6th term of -1, 3, -9, ...

Accepted Answer

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

Question 2

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 when n = 1.
For n = 1, we get 1   This is a true statement and Condition I is satisfied.
Next, we assume the statement holds for some k. That is,   is true for some positive integer k.
We need to show that the statement holds for k + 1. That is, we need to show that   So we assume that 1   is true and add the next term,   to both sides of the equation.   Condition II is satisfied. As a result, the statement is true for all natural numbers n.

Question 3

Find the indicated term using the given information.
--1 , 2 , 5 , ... ;

Accepted Answer

A) 104 
B) 107 
C) -106 
D) -109 
A) 104 
B) 107 
C) -106 
D) -109 A

Question 4

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary.
-

Accepted Answer

A) -732 
B) -2,460 
C) 69 
D) 240 
A) -732 
B) -2,460 
C) 69 
D) 240

Question 5

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

Accepted Answer

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

Question 6

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 the statement is true whe

Question 7

Find the sum of the sequence.
-

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

Find the sum of the sequence.
-

Accepted Answer

A) 101 
B) 110 
C) 68 
D) 42 
A) 101 
B) 110 
C) 68 
D) 42

Question 10

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary.
-

Accepted Answer

A) 726 
B) 1,230 
C) 87 
D) 24 
A) 726 
B) 1,230 
C) 87 
D) 24

Question 11

Find the sum.
-

Accepted Answer

A) -1,798 
B) -1,740 
C) -1,711 
D) -1,609.5 
A) -1,798 
B) -1,740 
C) -1,711 
D) -1,609.5

Question 12

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

Accepted Answer

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

Question 13

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary.
-4 + 12 + 36 + 108 + 324 + ... +

Accepted Answer

A) 13,120 
B) 13,100 
C) 13,157 
D) 13,122 
A) 13,120 
B) 13,100 
C) 13,157 
D) 13,122

Question 14

Find the sum.
-(-6)+ (-1)+ 4 + 9 + ... + 39

Accepted Answer

A) 165 
B) 170 
C) 160 
D) 330 
A) 165 
B) 170 
C) 160 
D) 330

Question 15

Expand the expression using the Binomial Theorem.
-

Accepted Answer

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

Question 16

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.
-

Accepted Answer

A) Geometric;   
B) Arithmetic; d   
C) Geometric; r = 6 
D) Neither 
A) Geometric;   
B) Arithmetic; d   
C) Geometric; r = 6 
D) Neither

Question 17

Solve.
-After working for 25 years you would like to have $800,000 in an annuity for early retirement. If theannual interest rate is 7.5%, compounded monthly, what will your monthly deposit need to be?

Accepted Answer

A) $911.93 
B) $2666.67 
C) $3088.48 
D) $1146.98 
A) $911.93 
B) $2666.67 
C) $3088.48 
D) $1146.98

Question 18

Express the sum using summation notation.
-

Accepted Answer

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

Question 19

Evaluate the expression.
-

Accepted Answer

A) 41,328 
B) 82,656 
C)    
D) 286 
A) 41,328 
B) 82,656 
C)    
D) 286

Question 20

Evaluate the factorial expression.
-

Accepted Answer

A) 479,001,600 
B) 132 
C) 24 
D) 16 
A) 479,001,600 
B) 132 
C) 24 
D) 16

Find the indicated term of the geometric sequence. -6th term of -1, 3, -9, ...

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. -

Find the indicated term using the given information. --1 , 2 , 5 , ... ;

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. -

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

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. -

Find the sum of the sequence. -

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

Find the sum of the sequence. -

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. -

Find the sum. -

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

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. -4 + 12 + 36 + 108 + 324 + ... +

Find the sum. -(-6)+ (-1)+ 4 + 9 + ... + 39

Expand the expression using the Binomial Theorem. -

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. -

Solve. -After working for 25 years you would like to have $800,000 in an annuity for early retirement. If theannual interest rate is 7.5%, compounded monthly, what will your monthly deposit need to be?

Express the sum using summation notation. -

Evaluate the expression. -

Evaluate the factorial expression. -

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Exam 9: Sequences; Induction; the Binomial Theorem

Find the indicated term of the geometric sequence. -6th term of -1, 3, -9, ...

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. -

Find the indicated term using the given information. --1 , 2 , 5 , ... ;

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. -

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

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. -

Find the sum of the sequence. -

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

Find the sum of the sequence. -

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. -

Find the sum. -

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

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. -4 + 12 + 36 + 108 + 324 + ... +

Find the sum. -(-6)+ (-1)+ 4 + 9 + ... + 39

Expand the expression using the Binomial Theorem. -

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. -

Solve. -After working for 25 years you would like to have $800,000 in an annuity for early retirement. If theannual interest rate is 7.5%, compounded monthly, what will your monthly deposit need to be?

Express the sum using summation notation. -

Evaluate the expression. -

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