Ques tion 1 (3 points)

Ques

tion 1 (3 points)

 

 

 

 

 

 

 

 

Q1. Using the general term an = 7n – 1, what is a75 ?

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Question 2 (3 points)

 

 

 

 

 

 

 

 

 

Q2. Using the general term an = n2 – 13n, what is the 19th term?

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Question 3 (3 points)

 

 

 

 

 

 

 

 

 

Q3. Evaluate {“version”:”1.1″,”math”:”<math xmlns=”http://www.w3.org/1998/Math/MathML”><munderover><mo>&#x2211;</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mn>6</mn></munderover></math>”} 4n2 – 7n.

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Question 4 (3 points)

 

 

 

 

 

 

 

 

 

Q4. What is a30 for the arithmetic sequence with a1 = 6 and d = 4?

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Question 5 (3 points)

 

 

 

 

 

 

 

 

 

Q5. Evaluate the arithmetic series{“version”:”1.1″,”math”:”<math xmlns=”http://www.w3.org/1998/Math/MathML”><munderover><mo>&#x2211;</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mn>100</mn></munderover><mstyle displaystyle=”false”></mstyle></math>”}8n + 7.

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Question 6 (3 points)

 

 

 

 

 

 

 

 

 

Q6. What is a10 for the geometric sequence with a1 = 3 and r = 2?

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Question 7 (3 points)

 

 

 

 

 

 

 

 

 

Q7

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7. Evaluate the geometric series 14*3n-1.

 

 

 

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Question 8 (3 points)

 

 

 

 

 

 

 

 

 

Q8. Suppose g1 = 1 and g2 = 3. The rest of the terms in a recursive sequence are given by the formula gn = n·gn-1 + gn-2.

Find the 7th term of the sequence, g7.

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Question 9 (3 points)

 

 

 

 

 

 

 

 

 

Q9. Consider the following algorithm:

sum = 0

For j starting at 1 and ending with 13:
sum = sum + (4*j + 6)

print(sum)

What is printed as a result of executing this algorithm?

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Question 10 (3 points)

 

 

 

 

 

 

 

 

 

Q10. Consider the following algorithm:

g1 = 7

g2 = 5

For k starting at 0 and ending with 8:

gk = (k-1)·gk-1 + gk-2

What is the last term, g8, of the recursive sequence generated as a result of executing this algorithm?

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Question 11 (3 points)

 

 

 

 

 

 

 

 

 

Q11. Let A = {1, 2, 3, 4, …, 12}. What is the cardinality of the power set of A, P(A)?

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Question 12 (3 points)

 

 

 

 

 

 

 

 

 

Q12. Fill in the missing element of B such that A = B.

A = {7, 19, g, #, 2, 4, &, f, 17, 1, k}

B = {#, 1, 7, __, k, 2, f, 19, g, 4, &}

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Question 13 (3 points)

 

 

 

 

 

 

 

 

 

Q13. Let A = {y ∈ Z : 10 {“version”:”1.1″,”math”:”<math style=”font-family:’Times New Roman'” xmlns=”http://www.w3.org/1998/Math/MathML”><mstyle mathsize=”18px”><mo>&lt;</mo></mstyle></math>”} y {“version”:”1.1″,”math”:”<math style=”font-family:’Times New Roman'” xmlns=”http://www.w3.org/1998/Math/MathML”><mstyle mathsize=”18px”><mo>&#x2264;</mo></mstyle></math>”} 14 and y is even}. What is |A|?

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Question 14 (3 points)

 

 

 

 

 

 

 

 

 

Q14D. Define the sets A, B, C, and D as follows:

A = {-3, 1, 6, 7, 10}
B = {-10, -5, 1, 4, 6}
C = {x ∈ Z: x is odd}
D = {x ∈ Z: x is positive}
Find A ∩ D.

*Express the set using roster notation and with values ordered smallest to largest, such as {-10, -3, 1, 6} (braces and commas are required; a space after each comma is also required).

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Question 15 (3 points)

 

 

 

 

 

 

 

 

 

Q15B. Define the sets A, B, C, and D as follows:

A = {y ∈ Z : 2 {“version”:”1.1″,”math”:”<math style=”font-family:’Times New Roman'” xmlns=”http://www.w3.org/1998/Math/MathML”><mstyle mathsize=”18px”><mo>&lt;</mo></mstyle></math>”} y {“version”:”1.1″,”math”:”<math style=”font-family:’Times New Roman'” xmlns=”http://www.w3.org/1998/Math/MathML”><mstyle mathsize=”18px”><mo>&#x2264;</mo></mstyle></math>”} 9 and y is odd}.
B = {1, 4, 6}
C = {y ∈ Z : y {“version”:”1.1″,”math”:”<math style=”font-family:’Times New Roman'” xmlns=”http://www.w3.org/1998/Math/MathML”><mstyle mathsize=”18px”><mo>&#x2264;</mo></mstyle></math>”} 10 and y is even}.
D = {y ∈ Z : y {“version”:”1.1″,”math”:”<math style=”font-family:’Times New Roman'” xmlns=”http://www.w3.org/1998/Math/MathML”><mstyle mathsize=”18px”><mo>&#x2264;</mo></mstyle></math>”} 7 and y is positive}
E = {-3, -1, 0, 5}
Find A ∪ E.

*Express the set using roster notation and with values ordered smallest to largest, such as {-10, -3, 1, 6} (braces and commas are required; a space after each comma is also required).

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Question 16 (3 points)

 

 

 

 

 

 

 

 

 

Q16D. Define the sets A and B as shown. Find {“version”:”1.1″,”math”:”<math xmlns=”http://www.w3.org/1998/Math/MathML”><menclose notation=”top”><mi>A</mi></menclose></math>”}.

*Express the set using roster notation and with letters ordered alphabetically, such as {d, n, x, z}.

(Braces and commas are required; a space after each comma is also required.)

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Question 17 (3 points)

 

 

 

 

 

 

 

 

 

Q17B. Define the sets A, B, C, and D as shown. Find A ∪ (B ∩ D).

*Express the set using roster notation and with letters ordered alphabetically, such as {d, n, x, z}.

(Braces and commas are required; a space after each comma is also required.)

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Question 18 (3 points)

 

 

 

 

 

 

 

 

 

Q18A. Define the sets A and B as shown. Select all statements which are true.

Question 18 options:

{a, f, g, h, m, s} ⊆ B

{a, c, m, p, s, w} ⊂ A

{m, s} ⊆ A

{a, g, s, m} ⊆ A

{a, f} ⊂ B

 

Question 19 (3 points)

 

 

 

 

 

 

 

 

 

Q19C. Define the sets A, B, C, and D as shown. Select all statements which are true.

Question 19 options:

D ⊆ B

{m, s} ⊂ C

{a, c, p, w} ⊂ A

{a, c, m, p, s, w} ⊂ A

C ⊆ B

 

Question 20 (3 points)

 

 

 

 

 

 

 

 

 

Q20. Suppose a computer program has been initialized such that the following sets have been stored for use in any algorithm:

A = {1, 2, 3, …, 47}
B = {-7, -6, -5, …, 30}

Consider the following algorithm, which represents one part of the whole computer program (comments may occur after the # symbol on any line and are not used in computations):

#Part 1: computes A – B and its cardinality

AminusB = set()
for element in A: # this line runs through every element in A
if not(element in B): #A – B is the set of elements that are in A and are not in B
AminusB.add(element) # Add to AminusB every element in A if the element is also not in B

n = len(AminusB) #len() returns the number of elements in the array
print(n)

 

What value is printed as a result of executing this algorithm?

Your Answer:

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