1/2,-4,32,-256 find an explicit formula for the sequence

This is a geometric sequence where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

an = a1 * r^n-1
where
an = nth term
a1 = 1st term
r = common ratio

In this problem, a1 = 1/2.

Find the common ratio by dividing -4 by 1/2 to get r = -8.

The explicit formula is an = (1/2)*(-4)^n-1