Question

Please help me on this problem! It has several parts. I will give a medal to the best response.

~Micah K.

Answer 1

Bill is able to save $35/week after working part-time and paying his expenses. These two formulas show his weekly savings:
f(1) = 35, f(n) = f(1) + f(n-1) for n > 1
f(n) = 35n
Which one of these formulas show the sequence written recursively and which shows it written explicitly? Justify your explanations.
Use the recursive formula to make a table of values for 1 ≤ n ≤ 5. Show your calculations. Explain what your table means.
Use any formula of your choice to find f(40). Explain why you chose that method and what your answer means. Show your calculations.
Given the sequence of numbers: 5, 6, 8, 11, 15, 20, 26, 33, 41,… Explain whether or not this sequence can be considered a function.

Answer 2

I think that I got the first part right. I answered by saying:

"The formula f(1) = 35, f(n) = f(1) + f(n-1) for n > 1 is recursive because each term is defined by the previous one. The formula f(n) = 35n is explicit because it's just a function/expression."