College Algebra questions

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

A. k + 5
B. k + 1
C. k + 3
D. k + 2

2) 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

3) 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

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

Find a50 when a1 = 7, d = 5

A. 192
B. 252
C. 272
D. 287

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

f1(x) = (x - 2)4

A. f1(x) = x4 - 5x3 + 14x2 - 42x + 26
B. f1(x) = x4 - 16x3 + 18x2 - 22x + 18
C. f1(x) = x4 - 18x3 + 24x2 - 28x + 16
D. f1(x) = x4 - 8x3 + 24x2 - 32x + 16

6) Write the first six terms of the following arithmetic sequence.

a1 = 5/2, d = - ½

A. 3/2, 2, 1/2, 1, 1/4, 0
B. 7/2, 2, 5/2, 1 ,3/2, 0
C. 5/2, 2, 3/2, 1, 1/2, 0
D. 9/2, 2, 5/2, 1, 1/2, 0

7) 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

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

(x2 + 2y)4

A. x8 + 8x6 y + 24x4 y2 + 32x2 y3 + 16y4
B. x8 + 8x6 y + 20x4 y2 + 30x2 y3 + 15y4
C. x8 + 18x6 y + 34x4 y2 + 42x2 y3 + 16y4
D. x8 + 8x6 y + 14x4 y2 + 22x2 y3 + 26y4

9) 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

10) 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

14) 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

15) 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

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

(2x3 - 1)4

A. 14x12 - 22x9 + 14x6 - 6x3 + 1
B. 16x12 - 32x9 + 24x6 - 8x3 + 1
C. 15x12 - 16x9 + 34x6 - 10x3 + 1
D. 26x12 - 42x9 + 34x6 - 18x3 + 1

19) 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

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

an = 3n + 2

A. 4, 6, 10, 14
B. 6, 9, 12, 15
C. 5, 8, 11, 14
D. 7, 8, 12, 15