ACT Practice Question: Sequences with a Pattern

 
Here is a practice question on sequences where you need to identify a repeating pattern.

When the fraction $\dfrac{4}{7}$ is written in the decimal form, what is the $277$th digit to the right of the decimal point?

1. $\quad 1$
2. $\quad 2$
3. $\quad 5$
4. $\quad 7$
5. $\quad 8$