If this an arithmetic sequence, then the first term a=1, second term a+d=1/2 and third term a+2d=1/4. So d from the second and third terms is 1/4-1/2=-1/4. However, d from the first and second terms is -1/2. Therefore the numbers are not in an arithmetic series.
If the series is geometric then r=1/2 and a=1, so the general term is (1/2)^n or 1/2^n and n starts from 0. If n starts from 1 the general term is (1/2)^(n-1).