Answer:
f(n) = 4 x 2^(n-1)
Explanation:
The general form of a geometric sequence is given by:
an = ar^(n-1)
where a is the first term, r is the common ratio, and n is the term number.
Using the given sequence, we can find the values of a and r:
a = 4
r = 8/4 = 2
Therefore, the function that generates this sequence is:
f(n) = 4 x 2^(n-1)
For example, when n = 1, f(1) = 4 x 2^(1-1) = 4 x 1 = 4, which is the first term of the sequence. When n = 2, f(2) = 4 x 2^(2-1) = 4 x 2 = 8, which is the second term of the sequence, and so on.