Question 1 of 20 | Mathematics homework help

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Question 1 of 20

The following are defined using recursion formulas. Write the first four terms of each sequence.

   a1 = 4 and an = 2an-1 + 3 for n ≥ 2

A. 4, 15, 35, 453

B. 4, 11, 15, 13

C. 4, 11, 25, 53                                                                                                                                

D. 3, 19, 22, 53

 

Question 2 of 20

Use the formula for the sum of the first n terms of a geometric sequence to solve the following.

Find the sum of the first 12 terms of the geometric sequence: 2, 6, 18, 54 . . .

A. 531,440

B. 535,450

C. 535,445

D. 431,440

 

Question 3 of 20

Write the first four terms of the following sequence whose general term is given.

 an = 3n

A. 3, 9, 27, 81

B. 4, 10, 23, 91

C. 5, 9, 17, 31

D. 4, 10, 22, 41

 

Question 4 of 20

If three people are selected at random, find the probability that at least two of them have the same birthday.

A. ≈ 0.07

B. ≈ 0.02

C. ≈ 0.01

D. ≈ 0.001

 

Question 5 of 20

A club with ten members is to choose three officers—president, vice president, and secretary-treasurer. If each office is to be held by one person and no person can hold more than one office, in how many ways can those offices be filled?

A. 650 ways

B. 720 ways

C. 830 ways

D. 675 ways

 

Question 6 of 20

Use the formula for the sum of the first n terms of a geometric sequence to solve the following.

Find the sum of the first 11 terms of the geometric sequence: 3, -6, 12, -24 . . .

A. 1045

B. 2108

C. 10478

D. 2049

 

Question 7 of 20

Use the Binomial Theorem to find a polynomial expansion for the following function.

 f1(x) = (x – 2)4

A. f1(x) = x4 – 5×3 + 14×2 – 42x + 26

B. f1(x) = x4 – 16×3 + 18×2 – 22x + 18

C. f1(x) = x4 – 18×3 + 24×2 – 28x + 16

D. f1(x) = x4 – 8×3 + 24×2 – 32x + 16

 

 

Question 8 of 20

An election ballot asks voters to select three city commissioners from a group of six candidates. In how many ways can this be done?

A. 20 ways

B. 30 ways

C. 10 ways

D. 15 ways

 

Question 9 of 20

Use the Binomial Theorem to expand the following binomial and express the result in simplified form.

 (2×3 – 1)4

A. 14×12 – 22×9 + 14×6 – 6×3 + 1

B. 16×12 – 32×9 + 24×6 – 8×3 + 1

C. 15×12 – 16×9 + 34×6 – 10×3 + 1

D. 26×12 – 42×9 + 34×6 – 18×3 + 1

 

Question 10 of 20

Find the indicated term of the arithmetic sequence with first term, a1, and common difference, d.

 Find a6 when a1 = 13, d = 4

A. 36

B. 63

C. 43

D. 33

 

Question 11 of 20

Find the indicated term of the arithmetic sequence with first term, a1, and common difference, d.

Find a200 when a1 = -40, d = 5

A. 865

B. 955

C. 678

D. 895

 

Question 12 of 20

Write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for an to find a20, the 20th term of the sequence.

 an = an-1 – 10, a1 = 30

A. an = 60 – 10n; a = -260

B. an = 70 – 10n; a = -50

C. an = 40 – 10n; a = -160

D. an = 10 – 10n; a = -70

 

Question 13 of 20

Write the first six terms of the following arithmetic sequence.

an = an-1 – 0.4, a1 = 1.6

A. 1.6, 1.2, 0.8, 0.4, 0, -0.4

B. 1.6, 1.4, 0.9, 0.3, 0, -0.3

C. 1.6, 2.2, 1.8, 1.4, 0, -1.4

D. 1.3, 1.5, 0.8, 0.6, 0, -0.6

 

Question 14 of 20

If 20 people are selected at random, find the probability that at least 2 of them have the same birthday.

A. ≈ 0.31

B. ≈ 0.42

C. ≈ 0.45

D. ≈ 0.41

 

 

 

Question 15 of 20

Consider the statement “2 is a factor of n2 + 3n.”

 If n = 1, the statement is “2 is a factor of __________.”

 If n = 2, the statement is “2 is a factor of __________.”

 If n = 3, the statement is “2 is a factor of __________.”

 If n = k + 1, the statement before the algebra is simplified is “2 is a factor of __________.”

 If n = k + 1, the statement after the algebra is simplified is “2 is a factor of __________.”

 

A. 4; 15; 28; (k + 1)2 + 3(k + 1); k2 + 5k + 8

B. 4; 20; 28; (k + 1)2 + 3(k + 1); k2 + 5k + 7

C. 4; 10; 18; (k + 1)2 + 3(k + 1); k2 + 5k + 4

D. 4; 15; 18; (k + 1)2 + 3(k + 1); k2 + 5k + 6

 

Question 16 of 20

How large a group is needed to give a 0.5 chance of at least two people having the same birthday?

A. 13 people

B. 23 people

C. 47 people

D. 28 people

 

Question 17 of 20

If two people are selected at random, the probability that they do not have the same birthday (day and month) is 365/365 * 364/365. (Ignore leap years and assume 365 days in a year.)

A. The first person can have any birthday in the year. The second person can have all but one birthday.

B. The second person can have any birthday in the year. The first person can have all but one birthday.

C. The first person cannot a birthday in the year. The second person can have all but one birthday.

D. The first person can have any birthday in the year. The second cannot have all but one birthday.

 

 

Question 18 of 20

k2 + 3k + 2 = (k2 + k) + 2 ( __________ )

A. k + 5

B. k + 1

C. k + 3

D. k + 2

 

Question 19 of 20

Write the first six terms of the following arithmetic sequence.

an = an-1 – 10, a1 = 30

 

A. 40, 30, 20, 0, -20, -10

B. 60, 40, 30, 0, -15, -10

C. 20, 10, 0, 0, -15, -20

D. 30, 20, 10, 0, -10, -20

 

Question 20 of 20

The following are defined using recursion formulas. Write the first four terms of each sequence.

a1 = 3 and an = 4an-1 for n ≥ 2

 

A. 3, 12, 48, 192

B. 4, 11, 58, 92

C. 3, 14, 79, 123

D. 5, 14, 47, 177

 

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