Use the recursively defined geometric sequence a1=56

Question

, an=4an−1
and find the common ratio.(1 point)
Responses

103
Start Fraction 10 over 3 End Fraction

4
4

56
Start Fraction 5 over 6 End Fraction

−23

Answer 1

In a geometric sequence, the common ratio \( r \) can be found by looking at the relationship between consecutive terms. Given the recursive definition of the sequence:

1. \( a_1 = 56 \)
2. \( a_n = 4a_{n-1} \)

From this, we can see that the relationship between term \( a_n \) and term \( a_{n-1} \) is defined by multiplying \( a_{n-1} \) by \( 4 \).

Thus, the common ratio \( r \) is \( 4 \).

So, the correct response is:

4