The ${20}^{th}$ term of an arithmetic sequence is ${\log }_{10}20 \text{and the }{32}^{\text{nd}}$ term is ${\log }_{10}32$. If exactly one term of the arithmetic sequence is a rational number which in lowest form is $\frac{p}{q}(p,q\in N) \text{then }(p+q)=......$