1. The problem asks for the middle term in the expansion of $ (p + q)^n $ where $ n $ is even. 2. Recall the binomial expansion formula: $$ (p + q)^n = \sum_{k=0}^n \binom{n}{k} p^{n-k} q^k $$ 3. Since $ n $ is even, the number of terms is $ n+1 $, which is odd, so there is a single middle term. 4. The middle term corresponds to the term where $ k = \frac{n}{2} $. 5. Therefore, the middle term is: $$ T_{\frac{n}{2}+1} = \binom{n}{\frac{n}{2}} p^{n-\frac{n}{2}} q^{\frac{n}{2}} = \binom{n}{\frac{n}{2}} p^{\frac{n}{2}} q^{\frac{n}{2}} $$ 6. This term is the coefficient $ \binom{n}{\frac{n}{2}} $ multiplied by $ p^{\frac{n}{2}} q^{\frac{n}{2}} $. Final answer: $$ \boxed{\binom{n}{\frac{n}{2}} p^{\frac{n}{2}} q^{\frac{n}{2}}} $$