Question 1

Express the sum using summation notation.
-

Accepted Answer

A)   
B)   
C)   
D)

Question 2

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.
-1, -3, 9, -27, 81, ...

Accepted Answer

A) Geometric; r = -3 
B) Geometric; r = 3 
C) Arithmetic; d = -4 
D) Neither

Question 3

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

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

Question 4

Write out the sum.
-

Accepted Answer

A)   
B)   
C) 0  
D)

Question 5

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum.
-16 + 8 + 4 + 2 + . . .

Accepted Answer

A) Converges; 32 
B) Converges; - 16 
C) Converges; 28 
D) Diverges

Question 6

Solve.
-During a five-year period, a company doubles its profits each year. If the profits at the end of the fifth yearare $160,000, then what are the profits for each of the first four years?

Accepted Answer

A) $10,000, $20,000, $40,000, $80,000 
B) $10,000, $20,000, $40,000, $100,000 
C) $11,000, $22,000, $44,000, $86,000 
D) $10,000, $20,000, $30,000, $40,000

Question 7

Solve the problem.
-The population of a town is increasing by 500 inhabitants each year. If its population at the beginning of1990 was 25,517, what was its population at the beginning of 1995?

Accepted Answer

A) 28,017 inhabitants 
B) 127,535 inhabitants 
C) 27,517 inhabitants 
D) 255,070 inhabitants

Question 8

Find the indicated term of the sequence.
-The ninth term of the arithmetic sequence 0, 11, 22, ...

Accepted Answer

A) 88 
B) 99 
C) 110 
D) 80

Question 9

Solve.
-A local civic theater has 22 seats in the first row and 21 rows in all. Each successive row contains 3additional seats. How many seats are in the civic theater?

Accepted Answer

A) 1092 seats 
B) 790 seats 
C) 1070 seats 
D) 1010 seats

Question 10

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) Arithmetic; d = -4 
B) Geometric; r = 3 
C) Arithmetic; d = 3 
D) Neither

Question 11

Expand the expression using the Binomial Theorem.
-

Accepted Answer

A)   
B)   
C) (  
D)

Question 12

Write out the first five terms of the sequence.
-

Accepted Answer

A)   
B)   
C)   
D)

Question 13

Find the sum.
-

Accepted Answer

A) 304.1 
B) 47.96 
C) 256.14 
D) 212.08

Question 14

Write out the first five terms of the sequence.
-

Accepted Answer

A)   
B)   
C)   
D)

Question 15

The given pattern continues. Write down the nth term of the sequence  suggested by the pattern.
-3 , 9 , 27, 81, 243 , ...

Accepted Answer

A)   
B)   
C)   
D)

Question 16

Solve.
-A basketball player signs a contract with a starting salary of $850,000 per year and an annual increase of6.5% beginning in the second year. What will the athleteʹs salary be, to the nearest dollar, in the sixth year?

Accepted Answer

A) $1,164,574 
B) $1,165,367 
C) $1,163,330 
D) $1,166,854

Question 17

Find the indicated term of the sequence.
-The eighteenth term of the arithmetic sequence

Accepted Answer

A)   
B)   
C)   
D)

Question 18

Solve.
-A particular substance decays in such a way that it loses half its weight each day. How much of thesubstance is left after 9 days if it starts out at 64 grams?

Accepted Answer

A)   gram 
B) 8 grams 
C)   gram 
D) 4 grams

Question 19

Solve.
-Use the Binomial Theorem to approximate  to 5 decimal places.

Accepted Answer

A) 0.88584 
B) 0.85841 
C) 0.88854 
D) 0.88548

Question 20

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

Accepted Answer

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

Exam 9: Sequences; Induction; the Binomial Theorem

Express the sum using summation notation. -

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. -1, -3, 9, -27, 81, ...

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. -

Write out the sum. -

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. -16 + 8 + 4 + 2 + . . .

Solve. -During a five-year period, a company doubles its profits each year. If the profits at the end of the fifth yearare $160,000, then what are the profits for each of the first four years?

Solve the problem. -The population of a town is increasing by 500 inhabitants each year. If its population at the beginning of1990 was 25,517, what was its population at the beginning of 1995?

Find the indicated term of the sequence. -The ninth term of the arithmetic sequence 0, 11, 22, ...

Solve. -A local civic theater has 22 seats in the first row and 21 rows in all. Each successive row contains 3additional seats. How many seats are in the civic theater?

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. -

Expand the expression using the Binomial Theorem. -

Write out the first five terms of the sequence. -

Find the sum. -

Write out the first five terms of the sequence. -

The given pattern continues. Write down the nth term of the sequence suggested by the pattern. -3 , 9 , 27, 81, 243 , ...

Solve. -A basketball player signs a contract with a starting salary of $850,000 per year and an annual increase of6.5% beginning in the second year. What will the athleteʹs salary be, to the nearest dollar, in the sixth year?

Find the indicated term of the sequence. -The eighteenth term of the arithmetic sequence

Solve. -A particular substance decays in such a way that it loses half its weight each day. How much of thesubstance is left after 9 days if it starts out at 64 grams?

Solve. -Use the Binomial Theorem to approximate to 5 decimal places.

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