In a geometric sequence, each term is obtained by multiplying the previous term by a constant factor called the common ratio.
In the given recursive definition of the sequence:
- \( a_1 = \frac{5}{6} \)
- \( a_n = 4 a_{n-1} \) for \( n > 1 \)
From the recursive relation, we can see that each term is obtained by multiplying the previous term by 4. Therefore, the common ratio \( r \) is:
\[ r = 4 \]
Thus, the common ratio of the geometric sequence is 4.