Help understanding relationship between sequences and partial sums

Question

I'll like to know the sequence a(n) associated with the following partial sum : s(n)= 1/2^n.

Firstly, i've found a(n) = -1/(2^n) (not sure if its entirely correct). Then by definition, s(1) = a(1), but s(1) = 1/2 and a(1) = -1/2.