little help please?
consider this function in recursive form
f(1)=-2 f(n)=4f(n-1) where n/- 2
select the equivalent explicit function for n /- 1

a. f(n)=-2n
b. f(n)=-2(n-1)
c. f(n)=-2(4)^n-1
d. f(n)=-2(n)^4

Question

little help please?
consider this function in recursive form
f(1)=-2 f(n)=4f(n-1) where n>/- 2
select the equivalent explicit function for n >/- 1

a. f(n)=-2n
b. f(n)=-2(n-1)
c. f(n)=-2(4)^n-1
d. f(n)=-2(n)^4

holsteremission · Answer

You can find the general rule for $f(n)$ by considering one value of the function at a time.

Start by finding $f(2)$. According to the formula, you should have
$$f(2)=4f(2-1)=4f(1)$$
Next, find $f(3)$. Well, you have again
$$f(3)=4f(3-1)=4f(2)=4(4(f(1))=4^2f(1)$$
Continue on and you should notice a distinct pattern. For any value of $n$, you can write $f(n)$ as a function of $f(1)$ times some power of $4$. What is the pattern?