Question 1

Find the sum of the infinite series.

Accepted Answer

A)    
B) 3 
C) undefined 
D)    
E)    
A)    
B) 3 
C) undefined 
D)    
E)

Question 2

Accepted Answer

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

Question 3

Calculate the binomial coefficient:

Accepted Answer

A) 342 
B) 38 
C) 1 
D) 0 
E) 171 
A) 342 
B) 38 
C) 1 
D) 0 
E) 171

Question 4

Find the sum.

Accepted Answer

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

Question 5

Find the indicated nth term of the geometric sequence. 4th term:

Accepted Answer

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

Question 6

Find the indicated nth term of the geometric sequence.

Accepted Answer

A) 29 
B) 20,480 
C) 81,920 
D) 62,500 
E) 312,500 
A) 29 
B) 20,480 
C) 81,920 
D) 62,500 
E) 312,500

Question 7

Write the first six terms of the sequence defined by the function. f(n) = 6n(n - 1)

Accepted Answer

A) -12, -36, 72, -120, -180, 0 
B) 12, 36, 72, 120, 180, 252 
C) 12, 36, 72, 120, 180, 504 
D) -12, 0, 36, 72, 120, 180 
E) 0, 12, 36, 72, 120, 180 
A) -12, -36, 72, -120, -180, 0 
B) 12, 36, 72, 120, 180, 252 
C) 12, 36, 72, 120, 180, 504 
D) -12, 0, 36, 72, 120, 180 
E) 0, 12, 36, 72, 120, 180

Question 8

Find the sum using the formulas for the sums of powers of integers.

Accepted Answer

A) -520 
B) -385 
C) -1560 
D) -135 
E) 600 
A) -520 
B) -385 
C) -1560 
D) -135 
E) 600

Question 9

Find the sum of the indicated terms of the geometric sequence. 3, 12, 48 ... (to 6 terms)

Accepted Answer

A) s = 4,095 
B) s = 4,098 
C) s = 4,101 
D) s = 4,092 
E) none of the above 
A) s = 4,095 
B) s = 4,098 
C) s = 4,101 
D) s = 4,092 
E) none of the above

Question 10

The probability that a basketball player will make a given free throw is   . To find the probability that the player makes exactly 8 out of her next 10 free throws, evaluate the term   in the expansion of   . Round to four decimal places.

Accepted Answer

A) 7.5497 
B) 0.0000 
C) 0.0001 
D) 0.3020 
E) 4.8318 
A) 7.5497 
B) 0.0000 
C) 0.0001 
D) 0.3020 
E) 4.8318

Question 11

Write the first six terms of the sequence defined by the function. f(n) = 9n(n - 1)

Accepted Answer

A) 0, 18, 54, 108, 180, 270 
B) 18, 54, 108, 180, 270, 756 
C) -18, -54, 108, -180, -270, 0 
D) -18, 0, 54, 108, 180, 270 
E) 18, 54, 108, 180, 270, 378 
A) 0, 18, 54, 108, 180, 270 
B) 18, 54, 108, 180, 270, 756 
C) -18, -54, 108, -180, -270, 0 
D) -18, 0, 54, 108, 180, 270 
E) 18, 54, 108, 180, 270, 378

Question 12

Several logs are stored in a pile with 22 logs on the bottom layer, 21 on the second layer, 20 on the third layer, and so on. If the top layer has one log, how many logs are in the pile?

Accepted Answer

A) 252 
B) 253 
C) 242 
D) 231 
E) none of the above 
A) 252 
B) 253 
C) 242 
D) 231 
E) none of the above

Question 13

Find the indicated nth partial sum of the arithmetic sequence. -2.1, 2.5, 7.1, 11.7, ...., n=90

Accepted Answer

A) -7996.5 
B) 18,241 
C) 18,648 
D) 18,227 
E) 18,234 
A) -7996.5 
B) 18,241 
C) 18,648 
D) 18,227 
E) 18,234

Question 14

Use the binomial theorem to expand the binomial.

Accepted Answer

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

Question 15

Evaluate the sum.

Accepted Answer

A) 2 
B) 84 
C) 5 
D) 42 
E) none of these 
A) 2 
B) 84 
C) 5 
D) 42 
E) none of these

Question 16

Find the indicated partial sum of the series.   third partial sum

Accepted Answer

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

Question 17

Determine whether the sequence is arithmetic. If so, find the common difference. 5, 25, 125, 625, 3125

Accepted Answer

A) 5 
B)   
C)    
D) -5 
E) not arithmetic 
A) 5 
B)   
C)    
D) -5 
E) not arithmetic

Question 18

Find the number of diagonals of a nonagon (9 sides). (A line segment connecting any two nonadjacent vertices is called a diagonal of the polygon.)

Accepted Answer

A) 27 
B) 72 
C) 81 
D) 9 
E) 18 
A) 27 
B) 72 
C) 81 
D) 9 
E) 18

Question 19

Use the binomial theorem to expand the binomial.

Accepted Answer

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

Question 20

Use summation notation to write the sum.

Accepted Answer

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

Find the sum of the infinite series.

Calculate the binomial coefficient:

Find the sum.

Find the indicated nth term of the geometric sequence. 4th term:

Find the indicated nth term of the geometric sequence.

Write the first six terms of the sequence defined by the function. f(n) = 6n(n - 1)

Find the sum using the formulas for the sums of powers of integers.

Find the sum of the indicated terms of the geometric sequence. 3, 12, 48 ... (to 6 terms)

The probability that a basketball player will make a given free throw is . To find the probability that the player makes exactly 8 out of her next 10 free throws, evaluate the term in the expansion of . Round to four decimal places.

Write the first six terms of the sequence defined by the function. f(n) = 9n(n - 1)

Several logs are stored in a pile with 22 logs on the bottom layer, 21 on the second layer, 20 on the third layer, and so on. If the top layer has one log, how many logs are in the pile?

Find the indicated nth partial sum of the arithmetic sequence. -2.1, 2.5, 7.1, 11.7, ...., n=90

Use the binomial theorem to expand the binomial.

Evaluate the sum.

Find the indicated partial sum of the series. third partial sum

Determine whether the sequence is arithmetic. If so, find the common difference. 5, 25, 125, 625, 3125

Find the number of diagonals of a nonagon (9 sides). (A line segment connecting any two nonadjacent vertices is called a diagonal of the polygon.)

Use the binomial theorem to expand the binomial.

Use summation notation to write the sum.

Functions and Their Graphs

Solving Equations and Inequalities

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Topics in Analytic Geometry

Algebraic Expressions and Equations

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Exam 9: Sequences, Series, and Probability

Find the sum of the infinite series.

Calculate the binomial coefficient:

Find the sum.

Find the indicated nth term of the geometric sequence. 4th term:

Find the indicated nth term of the geometric sequence.

Write the first six terms of the sequence defined by the function. f(n) = 6n(n - 1)

Find the sum using the formulas for the sums of powers of integers.

Find the sum of the indicated terms of the geometric sequence. 3, 12, 48 ... (to 6 terms)

The probability that a basketball player will make a given free throw is . To find the probability that the player makes exactly 8 out of her next 10 free throws, evaluate the term in the expansion of . Round to four decimal places.

Write the first six terms of the sequence defined by the function. f(n) = 9n(n - 1)

Several logs are stored in a pile with 22 logs on the bottom layer, 21 on the second layer, 20 on the third layer, and so on. If the top layer has one log, how many logs are in the pile?

Find the indicated nth partial sum of the arithmetic sequence. -2.1, 2.5, 7.1, 11.7, ...., n=90

Use the binomial theorem to expand the binomial.

Evaluate the sum.

Find the indicated partial sum of the series. third partial sum

Determine whether the sequence is arithmetic. If so, find the common difference. 5, 25, 125, 625, 3125

Find the number of diagonals of a nonagon (9 sides). (A line segment connecting any two nonadjacent vertices is called a diagonal of the polygon.)

Use the binomial theorem to expand the binomial.

Use summation notation to write the sum.

Functions and Their Graphs

Solving Equations and Inequalities

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Topics in Analytic Geometry

Algebraic Expressions and Equations

Filters