jmc

The arithmetic sequence 1, 3, 5, $\dots$, 17, has common difference 2, so the $n^{\text{th}}$ term is $1+2(n-1)=2n-1$. If $2n-1=17$, then $n=9$, so this arithmetic sequence contains 9 terms.

The sum of an arithmetic series is equal to the average of the first and last term, multiplied by the number of terms, so the sum is $(1+17)/2\cdot 9=\boxed{81}$.