In a geometric sequence, the common ratio \( r \) can be found from the recursive definition. Given the definition:
- \( a_1 = 56 \)
- \( a_n = 4a_{n-1} \)
The common ratio \( r \) is the factor by which we multiply the previous term to get the next term.
From the definition \( a_n = 4a_{n-1} \), we can see that:
- The second term \( a_2 = 4a_1 = 4 \times 56 = 224 \)
- The common ratio \( r = \frac{a_n}{a_{n-1}} = \frac{4a_{n-1}}{a_{n-1}} = 4 \)
So, the common ratio of this geometric sequence is \( 4 \).
Therefore, the answer is:
4