jmc

We begin filling in the table. The top row has a first term $1$ and a fifth term $25$, so we have the common difference is $\frac{25-1}{4}=6$. This means we can fill in the first row of the table: The fifth row has a first term of $17$ and a fifth term of $81$, so the common difference is $\frac{81-17}{4}=16$. We can fill in the fifth row of the table as shown: We must find the third term of the arithmetic sequence with a first term of $13$ and a fifth term of $49$. The common difference of this sequence is $\frac{49-13}{4}=9$, so the third term is $13+2\cdot 9=\boxed{31}$.