Create a vector called 'mathSequence' with the first $10$ terms of the Fibonacci sequence. Then

a$)$ Extend the sequence by adding the next $5$ Fibonacci numbers.

b$)$ Remove all even numbers from the sequence.

c$)$ Replace each number with its square root $($rounded to two decimal places$).$

d$)$ Find the sum of all elements in the vector.

e$)$ Determine if the golden ratio $($approximately $1\mathrm{.}618)$ exists between any two consecutive terms.

Design a program to perform the above operations. Explain how vectors simplify the process of working with mathematical sequences compared to traditional arrays. $(25$ MARKS$)$

$3\mathrm{.}23\mathrm{.}2$ Consider a doubly linked list storing student information $($name$,$ Student Number, DP$)$ with the following data: $($Alice$,40241001,67)<->($Bob$,40231002,84)<->($Charlie$,40221003,78)<->($David$,40201004,67)$ Perform these tasks:

a$)$ Add a new student $($Eve$,40231005,3\mathrm{.}6)$ to the end of the list.

b$)$ Remove the student with ID $40231002$ from the list.

c$)$ Swap the positions of the first and last students in the list.

d$)$ Sort the list based on DP in descending order.

e$)$ Find and print the name of the student with the highest DP$.$

Write C$++$ code to implement these operations and explain the advantages of using a doubly linked list in this scenario.