3. Fibonacci sequence Fibonacci sequence {n}nez+ satisfies the following conditions: fi = f2 = 1 fn = fn-1 + fn-2 for n 2 3 and n Z+ 3.1. [Python] Write a Python for loop to output the nth entry of the Fibonacci sequence. (@2%) 3.2. [Python] Write a Python recursive function fib() to output the fn given the input n. (@4%) 3.3. [Python] Consider the following sequence {bn}nez+: bn = Int2 forn Z+ Write a Python function seq2) to output bn given the input n. (@4%) 3.4. [Python] Consider the following Python code: for i in range (1,15,1): print (seq2 (i)) Please write down the output and compare b, with an in Problem 2. (Up to 6 decimal points) (@6%) 3.5. [Mathematics]Assuming bn Q, what is the value of p? (@2%) 3.6. [Mathematics] Consider a sequence {en}nezt, where cn = for n e Z+, write down the values of C1,C2,',C10, and compare with fu, f2,.,f10, and what is your observation about c; and fi. (@8%) 3.7. [Python] Write a Python function fib2() to calculate fn given the input n using your observation from 3.6. (@4%)