Question

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,

Answer 1

f(1) = 35
f(n) = f(1) + f(n-1)
so f(2)=f(1)+f(1)=35+35=70
f(3)=f(1)+f(2)=35+70=3*35
f(4)=f(1)+f(3)=35+3*35=4*35
...
f(n)=35*n

Answer 2

it is an arithmetic sequence
tn=t1+(n-1)d
with t1=35
d=35

Answer 3

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.