2013 AMC 10B Problem 13

Through the turn ending with $n$, the total number of numbers spoken is $$1+2+\cdots+n=\frac{n(n+1)}2.$$ After the turn ending with $9$, exactly $\frac{9\cdot10}{2}=45$ numbers have been spoken. The next turn is the list $1,2,\ldots,10$, so its eighth entry is the $53$rd number spoken. That entry is $8$. Thus, the correct answer is E .