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
1) Which one of these formulas show the sequence written recursively and which shows it written explicitly? Justify your explanations.
2) Use the recursive formula to make a table of values for 1 ≤ n ≤ 5. Show your calculations.
3) Use the explicit formula to demonstrate the most direct method to find f(40). Explain why you chose that method and what your answer means. Show your calculations.

Question

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
1)  Which one of these formulas show the sequence written recursively and which shows it written explicitly? Justify your explanations.
 2) Use the recursive formula to make a table of values for 1 ≤ n ≤ 5. Show your calculations.
   3) Use the explicit formula to demonstrate the most direct method to find f(40). Explain why you chose that method and what your answer means. Show your calculations.

anonymous · Answer

4) 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.