Instructions:

$$ Use this word document to complete the lab assignment.

$$ Complete all the questions in this document and upload the final word file to Moodle.

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$$ Upload the programming files $($in $.$java format$)$ to Moodle for individual questions.

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Objective: In this lab, you will implement a recursive function to calculate the Fibonacci series and explore how recursion can be used to solve problems with a recursive structure. You will also learn how to empirically calculate the computational time of a code.

Question $1$:

Write a Java program that includes a recursive function to calculate the Fibonacci series up to a given term. The Fibonacci series is defined as follows:

$$ The first two terms are $0$ and $1.$

$$ The subsequent terms are the sum of the two preceding terms.

Mathematically: F$(0)=0,$ F$(1)=1,$ and for n $>=2,$ F$($n$)=$ F$($n$-1)+$ F$($n$-2).$

Implement a recursive function called calculateFibonacci$($int n$)$ that calculates the nth term of the Fibonacci series using recursion.

In the main method, prompt the user to enter an integer n $($where n $>=0)$ and then call the calculateFibonacci function to compute and display the nth term of the Fibonacci series. The program should not accept non$-$negative integer n and an error message must be displayed. The program should also calculate and display the time it takes to complete execution $($Hint: Use System.nanoTime to get current time snapshot in nanoseconds$).$

Complete the following table using your program:

Integer n Fibonacci Sequence $($F$($n$))$ Elapsed Time $($s$)$

$1$

$3$

$5$

$10$

$15$

$20$

Insert your Java code in the box below. Also, submit the java code on Moodle.