Question

Use the recursively defined geometric sequence a1=56
, an=4an−1
and find the common ratio.(1 point)
Responses

4
4

103
Start Fraction 10 over 3 End Fraction

−23
negative Start Fraction 2 over 3 End Fraction

56

Answer 1

In a geometric sequence, each term is found by multiplying the previous term by a common ratio. The sequence you provided is defined recursively as follows:

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

From this definition, we can see that to get from one term to the next, we multiply by 4.

Thus, the common ratio \(r\) is:

\[
r = 4
\]

So, the answer is **4**.