Please Help Me Check My Work :)

Question

1) Find the 5th term of - f(n)= 3(n-3)
My answer- -279

2) Find the third term if the first term is 4 - f(n)= 2f(n-1)+2
My answer- 16

3) Find the third term using the explicit rule - f(n) 4-n/n+3
My answer- 1/6

4) Recursive Function- 1, -2, -5, -8 Find the next 4 numbers and find the function.
My answer- Sequence= 4-3n ; next 4 numbers = 28, -80, 244, -728

Thank you!!

Answer 1

#1 If you mean

f(n) = 3(n-3) then f(5) = 3(5-3) = 6
f(n) = 3^(n-3) then f(5) = 3^2 = 9
f(n) = 3^n - 3 then f(5) = 3^5-3 = 240
How did you come up with 279?

#2
f(n) = 2f(n-1)+2
f(1) = 4
f(2) = 2(4)+2 = 10
f(3) = 2(10)+2 = 22

#3 f(n) = (4-n)/(n+3)
f(3) = (4-3)/(3+3) = 1/6

#4 I like 4-3n
But, that means each term is just 3 less than the previous one:

1 -2 -5 -8 -11 -14 -17 ...

Your numbers appear to be 1-(-3)^n