Question 1

Evaluate the factorial expression.
-

Accepted Answer

A) 4 
B) 1 
C)   
D)

Question 2

Solve.
-Use the Binomial Theorem to approximate  to 7 decimal places.

Accepted Answer

A) 1.0510101 
B) 1.050101 
C) 1.0550101 
D) 1.0550505

Question 3

Find the sum of the sequence.
-

Accepted Answer

A) 176 
B) 56 
C) 88 
D) 120

Question 4

Find the sum.
-1 + 3 + 5 + ... + 539

Accepted Answer

A) 72,900 
B) 73,170 
C) 73,441 
D) 72,361

Question 5

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary.
--8 - 24 - 72 - 216 - 648 - ... -

Accepted Answer

A) -236,192 
B) -236,212 
C) -236,155 
D) -236,190

Question 6

Use the Binomial Theorem to find the indicated coefficient or term.
-The 7th term in the expansion of

Accepted Answer

A)   
B)   
C)   
D)

Question 7

Write out the sum.
-

Accepted Answer

A)   
B)   
C)   
D)

Question 8

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

Accepted Answer

A) 3276.6 
B) 3276.4 
C) 6553.2 
D) 6553.4

Question 9

Solve.
-The number of students in a school in year n is estimated by the model  . About howmany students are in the school in each of the first three years?

Accepted Answer

A) 98, 123, 156 
B) 111, 136, 169 
C) 102, 123, 156 
D) 98, 123, 144

Question 10

Solve.
-After being struck with a hammer, a gong vibrates 45 vibrations in the first second and in each secondthereafter makes  as many vibrations as in the previous second. Find how many vibrations the gongmakes before it stops vibrating.

Accepted Answer

A) 270 vibrations 
B) 54 vibrations 
C) 280 vibrations 
D) 49 vibrations

Question 11

Solve.
-A pendulum bob swings through an arc 80 inches long on its first swing. Each swing thereafter, it swingsonly 66% as far as on the previous swing. What is the length of the arc after 9 swings? Round your answerto two decimal places, if necessary.

Accepted Answer

A) 2.88 inches 
B) 1.9 inches 
C) 1.25 inches 
D) 422.4 inches

Question 12

Find the sum.
-7 + 14 + 21 + ... + 770

Accepted Answer

A) 42735 
B) 42350 
C)   
D) 41965

Question 13

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

Accepted Answer

A) Converges;  
B) Converges; 1 
C) Converges;  
D) Diverges

Question 14

Write the word or phrase that best completes each statement or answers the question.
-A wildlife refuge currently has 100 deer in it. A local wildlife society decides to add an additional 2 deereach month. It is already known that the deer population is growing 12% per year. The size of thepopulation is given by the recursively defined sequence  How many deer are in the wildlife refuge at the end of the second month? That is, what is

Accepted Answer

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

Question 15

Write the word or phrase that best completes each statement or answers the question.
-Initially, a pendulum swings through an arc of 3 feet. On each successive swing, the length of the arc is 0.8of the previous length. After 10 swings, what total length will the pendulum have swung (to the nearesttenth of a foot)?

Accepted Answer

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

Question 16

Write out the first five terms of the sequence.
-

Accepted Answer

A)   
B)   
C)   
D)

Question 17

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.
-Use the Principle of Mathematical Induction to show that the statement ʺ5 is a factor of  ʺ is true forall natural numbers. (

Accepted Answer

The answer of  Mathematical Induction
1 Prove Statements Using Mathematical...

Question 18

Write out the first five terms of the sequence.
-

Accepted Answer

A)   
B)   
C)   
D)

Question 19

Express the sum using summation notation.
-

Accepted Answer

A)   
B)   
C)   
D)

Question 20

Write out the sum.
-

Accepted Answer

A) 12 + 15 + 18 + ... + (3n + 9) 
B) 3n + 9 
C) 9 +12 + 15 + ... + (3n + 9) 
D) 1 + 2 + 3 + ... + n

Exam 9: Sequences; Induction; the Binomial Theorem

Evaluate the factorial expression. -

Solve. -Use the Binomial Theorem to approximate to 7 decimal places.

Find the sum of the sequence. -

Find the sum. -1 + 3 + 5 + ... + 539

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. --8 - 24 - 72 - 216 - 648 - ... -

Use the Binomial Theorem to find the indicated coefficient or term. -The 7th term in the expansion of

Write out the sum. -

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

Solve. -The number of students in a school in year n is estimated by the model . About howmany students are in the school in each of the first three years?

Solve. -After being struck with a hammer, a gong vibrates 45 vibrations in the first second and in each secondthereafter makes as many vibrations as in the previous second. Find how many vibrations the gongmakes before it stops vibrating.

Solve. -A pendulum bob swings through an arc 80 inches long on its first swing. Each swing thereafter, it swingsonly 66% as far as on the previous swing. What is the length of the arc after 9 swings? Round your answerto two decimal places, if necessary.

Find the sum. -7 + 14 + 21 + ... + 770

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

Write out the first five terms of the sequence. -

Write out the first five terms of the sequence. -

Express the sum using summation notation. -

Write out the sum. -