first of all, notice your primary exponent of n has to be one less than the term number

so lets start with 2^(n-1)

to give us 1,2,4,8,....

now you want to make all odd-numbered terms to have a negative exponent

Your (-1)^n does that perfectly.

so you were very close,

Term(n) = 2^((n-1)(-1)^n)