To find the sum of \( p \) and \( q \) where \( p = 34 \) and \( q = -114 \), you can perform the following calculation:
\[ p + q = 34 + (-114) \]
This simplifies to:
\[ 34 - 114 = -80 \]
So the sum of \( p \) and \( q \) is \( -80 \).
Since \(-80\) is already in its simplest form, there is no need to reduce the answer further. Thus, the final answer is:
\[ \boxed{-80} \]