In Java,

You will create a recursive function and an iterative function for each of the following problems.

Write a function that takes an integer $$n$$ and returns the sum of the first n natural numbers. The first $$n$$ natural numbers are defined as positive integers less than or equal to $$n$.$ For example, the sum of the first $5$ natural numbers is $1+2+3+4+5=15.$

Write a function that takes an integer $$n$$ and returns the nth number in the sequence $1,1,2,4,7,13,24,44,...$ where each number is the sum of the three preceding it$.$

Write a function that takes an integer n and returns the product of the first n even numbers. For example, the product of the first $5$ even numbers is $2*4*6*8*10=3840.$