Given a sequence ($u_1; u_2; u_3;...; u_n$), $n\in \mathbb{N}$, of $n$ terms in geometric series, show that for every natural number $0\le p\le n-1$,
$$u_{1+p} \cdot u_{n-p}=u_1 \cdot u_n$$
I know I'm not supposed to ask for solutions for textbooks exercises, but I'm teaching myself math without ever have had a math class in highschool. I would appreciate not only a solution but an intuitive description.