Hello, I must complete the following review questions as it will greatly help me with my upcoming exam. The topic for this assignment is Recurrence Relations and its for my ICS course. Thank you so much

(4)]. List the a; and a3 terms of the sequence dened by the following recurrence relation and initial conditions. an : 4am1 + 2an_2, a0 = 3, a1 = 4 (2)2. Find a solution to the following recurrence relation and initial condition. an = 2a,,,_l,w0 = 3 (3)3.a. Suppose the number of bacteria in a colony quadruples every hour. Set up a recurrence relation for the number of bacteria in the colony at the end of n hours. 3.b. Find an explicit formula for the number of bacteria remaining in the colony after n hours. 3.c. If 80 bacteria form a new colony, how many will be in the colony after three hours? (2)4. A message can be transmitted over a network using a combinations of signals that either require one microsecond or two microseconds. Set up a recurrence relation for the number of different messages that can be transmitted in n microseconds. (3)5. A vending machine takes $1 bills, $1 tokens, $2 tokens and $5 tokens. Find a recurrence relation for the number of ways to insert $n in the machine where the order matters. (3)6. How many positive integers less than 500 are either divisible by 5 or by 1 1? (3)7. Suppose that 80 community delegates discussed the transportation problems on Oahu. 30 of them favor expanding the bus system, 34 favor introduction of rail, and 44 favor building more highways. 15 favor a combination including at least bus expansion and rail, 22 favor a combination including at least rail and more highways, and 21 favor a combination including at least more highways and an expanded bus system, while 12 favor a combination of all three strategies. a. How many favor only adding more highways? b. How many favor a combination of an expanded bus system and rail? c. How many do not like any of the three alternatives