Q11-5 points How many (5 digit) U.S. zip codes are possible, assuming that every possible 5-digit sequence can be used as a valid zip code?

Q17-5 points Solve by backtracking for an explicit formula for the recursive sequence: a1​ = 4 an​ = -3a​n-1

Q16-5 points Use the Binomial Theorem to write out the expansion of (a + b)4 .

Q13-5 points Jim has a drawer with 6 red socks, 6 blue socks, and 10 black socks. If he picks them out without looking, how many socks must Jim pull out of the drawer to guarantee that he has a matching color pair?

Q19-5 points Consider the sequence: 1, 7, 13, 19, 25, … Find both the 50th term of the sequence and the sum of the first 50 terms.

Q18-5 points Solve the recurrence relation: b1​ = 2 b2​ = 6​ bn​ = 2​bn-1​ −​ b​n-2

Q9-5 points Use the roster method to describe the set  { 3n | n ∈ ℤ }.

Q1-6 points Let ​p​ = “The sky is blue.” Let ​q​ = “The sky is cloudy.” Convert into symbols:   “If the sky is blue, then the sky is not cloudy.”

Q7-5 points Let D  = ​{1, 4, 6, 7, 8}. How many subsets of size 3 does D have?

Q12-8 points Let ​n be an integer. Use a proof by contrapositive to prove that if ​3n²​ is odd, then ​n​ is odd.