# Algebra 20

1of 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

 2 of 20 5.0 Points

The following are defined using recursion formulas. Write the first four terms of each sequence.  a1 = 7 and an = an-1 + 5 for n ≥ 2

A. 8, 13, 21, 22

B. 7, 12, 17, 22

C. 6, 14, 18, 21

D. 4, 11, 17, 20

 3 of 20 5.0 Points

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

 4 of 20 5.0 Points

Write the first six terms of the following arithmetic sequence.  an = an-1 + 6, a1 = -9

A. -9, -3, 3, 9, 15, 21

B. -11, -4, 3, 9, 17, 21

C. -8, -3, 3, 9, 16, 22

D. -9, -5, 3, 11, 15, 27

 5 of 20 5.0 Points

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

 6 of 20 5.0 Points

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

 7 of 20 5.0 Points

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

 8 of 20 5.0 Points

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

A. k + 5

B. k + 1

C. k + 3

D. k + 2

 9 of 20 5.0 Points

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

 10 of 20 5.0 Points

To win at LOTTO in the state of Florida, one must correctly select 6 numbers from a collection of 53 numbers (1 through 53). The order in which the selection is made does not matter. How many different selections are possible?

A. 32,957,326 selections

B. 22,957,480 selections

C. 28,957,680 selections

D. 225,857,480 selections

 11 of 20 5.0 Points

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

 12 of 20 5.0 Points

You volunteer to help drive children at a charity event to the zoo, but you can ﬁt only 8 of the 17 children present in your van. How many different groups of 8 children can you drive?

A. 32,317 groups

B. 23,330 groups

C. 24,310 groups

D. 25,410 group

 13 of 20 5.0 Points

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.

 14 of 20 5.0 Points

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

 15 of 20 5.0 Points

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

 16 of 20 5.0 Points

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

 17 of 20 5.0 Points

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

 18 of 20 5.0 Points

Use the Binomial Theorem to expand the following binomial and express the result in simpliﬁed form. (x2 + 2y)4

A. x8 + 8×6 y + 24×4 y2 + 32×2 y3 + 16y4

B. x8 + 8×6 y + 20×4 y2 + 30×2 y3 + 15y4

C. x8 + 18×6 y + 34×4 y2 + 42×2 y3 + 16y4

D. x8 + 8×6 y + 14×4 y2 + 22×2 y3 + 26y4

 19 of 20 5.0 Points

If three people are selected at random, find the probability that they all have different birthdays.

A. 365/365 * 365/364 * 363/365 ≈ 0.98

B. 365/364 * 364/365 * 363/364 ≈ 0.99

C. 365/365 * 365/363 * 363/365 ≈ 0.99

D. 365/365 * 364/365 * 363/365 ≈ 0.99

 20 of 20 5.0 Points

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
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