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The nth triangle number of the ?rst six

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The nth triangle number of the ?rst six. Provide a single program consists of the following: 0 Write a function called TriangulaIRe cursive for the recursive version that takes num- ber of level as an int argument. Hints: 1} Identifyr the base case for the Triangular?ecursive function. 2} Let the TriangularRecuraive function call itself, with proper arguments. I: Write a function called TriangularIterat ive for the non-recursive (iterative) version that takes number of level as an int argument. - Write a main function that calls the two functions inside. You should have at least a couple of test cases included in the main function that shows the output for both functions. After implementing the recursive and non—recursive functions, you are supposed to perform two additional tasks. The ?rst task is to analyze both approaches as follows: a Establish the recurrence relations for the recursive approach. - Solve the recurrence and provide the order growth. - Establish the sum expression for the non—recursive approach. a Solve the sum and provide the order growth. The second task is to plot the running time of both approaches for different input sizes (in). To do that, consider ten input size [11:] values: 10, 50, 100, 20!}, 400, 300, 2000, 40m}, 3000, IUDEH}. For better precision, run each value ten times and take the average of all ten runs for each case.