2015 Gauss 8 Problem 17

When expressed as a repeating decimal, the fraction \frac{1}{7} is written as 0.142857142857\ldots (The 6 digits 142857 continue to repeat.) The digit in the third position to the right of the decimal point is 2. In which one of the following positions to the right of the decimal point will there also be a 2?

\textbf{(A)}\ 119^{th}\quad \textbf{(B)}\ 121^{st}\quad \textbf{(C)}\ 123^{rd}\quad \textbf{(D)}\ 125^{th}\quad \textbf{(E)}\ 126^{th}

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.