Question

Bill is able to save $35/week after working part-time and paying his expenses. These two formulas show his weekly savings: A.f(1) = 35, f(n) = f(1) + f(n-1) for n > 1
B.f(n) = 35n I.Which one of these formulas show the sequence written recursively, and which shows it written explicitly? Justify your explanations.II.Use the recursive formula to make a table of values for 1 ≤ n ≤ 5. Show your calculations. Explain what your table means.
III.Use any formula of your choice to find f(40). Explain why you chose that method and what your answer means. Show your calculations.IV. Given the sequence

Answer 1

the recursive one is f(n)=f(n-1)+f(1)
because we have the expenses for the next week
f(2)=f(1)+f(1)=70
then we take that f(3)=f(2)+f(1)
so each time we take the previous expenses add to it the first weeks expenses

Answer 2

the second one is the explicit formula for the expense
knowing that for week 1(n=1)
we start with f(1)=35
for f(2)=35x2
for any week we place into the formula the index of the week to obtain the new home expenses for that given week

Answer 3

the other part just look at your notes for more details on tables
and things like that!
you should have done this with functions

Answer 4

so I would take f(3)=f(2)+f(1) and add it to f(n) = f(1) + f(n-1

Answer 5

or not help that's cool with me to :)

Answer 6

No! that's not what i said
the formula is f(n)=f(n-1)+f(1)
if i asked you how much are the expenses are in year 2
using our formula we should be able to know
we just plug in 2 for n
f(2)=f(2-1)+f(1)=f(1)+f(1)
and we already know about the expenses for the first years
f(1)=35$ hence f(2)=35+35=70
that's recursively meaning each year i have the original expenses 35$
add to that the previous expenses for the previous year
for n=3 the third year the expenses are f(3)=f(2)+f(1)=70+35

Answer 7

thankyou but I figured it out.

Answer 8

alright good luck