This is a geometric sequence with a common ration of half (1/2)
The general formula of a geometric sequence, with common ratio r, first term a
at the nth term, is given by
[tex]\begin{gathered} U_n=ar^{n-1} \\ a=-64, \\ r=\frac{-32}{-64}=\frac{1}{2} \\ \text{Therefore} \\ U^{}_n=-64\times(\frac{1}{2})^{n-1}=-1\times2^6\times2^{-(n-1)}^{}=-1\times2^{-n+1+6}=(-1)2^{-n+7}_{} \\ \text{Therefore the explicit formula is} \\ U_n=(-1)2^{7-n} \end{gathered}[/tex]