To find the sum of \( p \) and \( q \), where \( p = 34 \) and \( q = -114 \), we can perform the following calculation:
\[ p + q = 34 + (-114) \] This simplifies to:
\[ p + q = 34 - 114 = -80 \]
Thus, the sum of \( p \) and \( q \) is \( -80 \). Since this number is already in its lowest terms, the final answer is:
\[ \boxed{-80} \]