Suppose $\alpha$ and $\beta$ be two real roots of $x^2-px+q=0$ where $p$ and $q\ne 0$ are two real numbers. Let sequence $\{a_n\}$ satisfies $a_1=p$, $a_2=p^2-q$, and $a_n=pa_{n-1}-qa_{n-2}$ for $n > 2$.

Express $a_n$ using $\alpha$ and $\beta$.

If $p=1$ and $q=\frac{1}{4}$, find the sum of first $n$ terms of $\{a_n\}$.