Fall 2020
1) For the following sequence, determine if it is an arithmetic sequence, a geometric sequence, or neither. If it is either arithmetic or geometric, give the next term in the sequence.
4, 9, 14, 19, 24, …
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
a) The sequence is geometric. The next term is 4, 9, 14, 19, 24, _________ .
b) The sequence is arithmetic. The next term is 4, 9, 14, 19, 24, __________ .
c) The sequence is neither arithmetic nor geometric.
2) A bass guitarist worked on 8 music projects last year. He wrote and produced 2 projects. He wrote a total of 3 projects. He produced a total of 7 projects. Use a Venn diagram to determine (a) how many projects he wrote but did not produce, and (b) how many projects he produced but did not write.
Complete the Venn diagram. Let W be the set of projects the bass guitarist wrote and P be the set of projects he produced.
a) How many projects did he write but not produce?
______ project(s)
(Type a whole number.)
b) How many projects did he produce but not write?
______ project(s)
(Type a whole number.)
3) Construct a truth table for the given statement. Identify whether the statement is a tautology.
(q ∧ p) → (p ∧ q)
Is the statement a tautology?
a) The statement is not a tautology, since it is false for all combinations of truth values of the components.
b) The statement is a tautology, since it is true for all combinations of truth values of the components.
c) The statement is not a tautology, since there is at least one combination of truth values for its components where the statement is false.
d) The statement is a tautology, since there is at least one combination of truth values for its components where the statement is true.
4) Convert the number to decimal form.
232eight
a) 56
b) 1232
c) 240
d) 154
5) Use the method of dividing by prime factors to find the least common multiple of 75 and 105.
The LCM of 75 and 105 is _______.
