jmc

An arithmetic sequence is formed by adding the common difference to each term to find the next term. Thus, the common difference must evenly divide the difference $91-1=90$. Each factor of 90 will correspond to one possible sequence. For example, the factor 30 corresponds to the sequence $1,31,61,91,...$. So, we need to count the factors of 90. Factoring, we find: $$90=2\cdot 3^2\cdot 5$$ So, 90 has: $$(1+1)(2+1)(1+1)=12\text{ factors}$$ This corresponds to $\boxed{12}$ possible sequences.