In a geometric sequence, the common ratio \( r \) is defined as the factor by which we multiply one term to get the next term in the sequence.
Given the recursively defined sequence:
- \( a_1 = 56 \)
- \( a_n = 4a_{n-1} \)
To find the common ratio, let's look at how one term relates to the previous term:
\[ a_2 = 4a_1 = 4 \times 56 = 224 \]
Now, the common ratio \( r \) can be calculated as follows:
\[ r = \frac{a_2}{a_1} = \frac{224}{56} = 4 \]
Thus, the common ratio of the geometric sequence is \( 4 \).
The correct response is:
4
1 answer