Question 1

Use summation notation to write the sum below.

Accepted Answer

A)   
B)   
C)   
D)   
E)    E

Question 2

Find the sum of the finite geometric series.

Accepted Answer

A)   
B)   
C)   
D)   
E)    A

Question 3

Find the indicated term of the sequence.

Accepted Answer

A)   106
B)   -110
C)   -122
D)   18
E)   -112 B

Question 4

Find the sum of the infinite geometric series below.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 5

Find the probability for the experiment of drawing two marbles (without replacement) from a bag containing two green, three yellow, and four red marbles such that the marbles are different colors.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 6

Evaluate the series.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 7

Find the number of distinguishable permutations of the group of letters.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 8

Use the Binomial Theorem to expand the expression.Simplify your answer.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 9

Calculate the binomial coefficient:

Accepted Answer

A)   60
B)   15
C)   10
D)   1
E)   0

Question 10

Write the rational number  as the quotient of two integers in simplest form.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 11

Evaluate the binomial coefficient.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 12

You are given the probability that an event will not happen.Find the probability that the event will happen.

Accepted Answer

A)   
B)   0
C)   1
D)   
E)

Question 13

Find the rational number representation of the repeating decimal.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 14

A heavy object (with negligible air resistance) is dropped from a plane.During the first second of fall, the object falls 16.6 meters; during the second second, it falls 49.8 meters; during the third second, it falls 83.0 meters; and during the fourth second, it falls 116.2 meters.If this pattern continues, how many meters will the object fall in 10 seconds?

Accepted Answer

A)   813.4 meters
B)   597.6 meters
C)   1062.4 meters
D)   1660.0 meters
E)   1344.6 meters

Question 15

The annual profit  (in millions of dollars) for a certain company from 2000 to 2005 can be approximated by the model   where  represents the year, with  corresponding to 2000.Use the formula for the sum of a finite geometric sequence to approximate the total profit earned during this six-year period.Round to the nearest ten-thousand dollars.

Accepted Answer

A)   $4466.74 million
B)   $4805.90 million
C)   $3631.55 million
D)   $3292.39 million
E)   $2676.77 million

Question 16

Determine whether the sequence is geometric.If so, find the common ratio. -5, -2, 1, 4, ...

Accepted Answer

A)   3
B)   -5
C)   
D)   -3
E)   not geometric

Question 17

Assume that the probability of the birth of a child of a particular gender is 50%.In a family with eight children, what is the probability that there is at least one girl?

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 18

Write the first five terms of the geometric sequence.

Accepted Answer

A)   -5, -2, 1, 4, 7
B)   -5, -15, -45, -135, -405
C)   
D)   
E)

Question 19

Use a graphing utility to graph the first 10 terms of the sequence.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 20

Use the Binomial Theorem to expand the complex number.Simplify your result.

Accepted Answer

A)   -112 - 384i
B)   -112 + 384i
C)   112 - 384i
D)   112 + 384i
E)   256

Exam 7: Sequences, Series, and Probability

Use summation notation to write the sum below.

Find the sum of the finite geometric series.

Find the indicated term of the sequence.

Find the sum of the infinite geometric series below.

Find the probability for the experiment of drawing two marbles (without replacement) from a bag containing two green, three yellow, and four red marbles such that the marbles are different colors.

Evaluate the series.

Find the number of distinguishable permutations of the group of letters.

Use the Binomial Theorem to expand the expression.Simplify your answer.

Calculate the binomial coefficient:

Write the rational number as the quotient of two integers in simplest form.

Evaluate the binomial coefficient.

You are given the probability that an event will not happen.Find the probability that the event will happen.

Find the rational number representation of the repeating decimal.

Determine whether the sequence is geometric.If so, find the common ratio. -5, -2, 1, 4, ...

Assume that the probability of the birth of a child of a particular gender is 50%.In a family with eight children, what is the probability that there is at least one girl?

Write the first five terms of the geometric sequence.

Use a graphing utility to graph the first 10 terms of the sequence.

Use the Binomial Theorem to expand the complex number.Simplify your result.