Use the recursively defined geometric sequence a1=5/6

Question

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

−2/3
negative Start Fraction 2 over 3 End Fraction

5/6
Start Fraction 5 over 6 End Fraction

10/3
Start Fraction 10 over 3 End Fraction

4

Answer 1

To determine the common ratio of the given geometric sequence defined by the recursion $a_1=\frac{5}{6}$ and $a_n=4a_{n-1}$, we can analyze the expression for $a_n$.

In a geometric sequence, the common ratio $r$ is defined as the factor by which we multiply one term to get to the next term. Here, the recursive formula indicates that each term is obtained by multiplying the previous term $a_{n-1}$ by 4:

$$r=4$$

Thus, the common ratio of this geometric sequence is:

$$\boxed{{\displaystyle 4}}$$