Question

Use the recursively defined geometric sequence a1=5/6 , an=4an−1 and find the common ratio.(1 point)

Answer 1

Use the recursively defined geometric sequence a1=5/6 , an=4an−1 and find the common ratio.(1 point)
Responses

103
Start Fraction 10 over 3 End Fraction

4
4

−23
negative Start Fraction 2 over 3 End Fraction

56

Answer 2

In a geometric sequence, the common ratio \( r \) is the factor by which each term is multiplied to get the next term. Given the recursively defined geometric sequence:

- \( a_1 = \frac{5}{6} \)
- \( a_n = 4 a_{n-1} \)

We can see that each term is obtained by multiplying the previous term by 4. Thus, the common ratio \( r \) is:

\[
r = 4
\]

So, the common ratio of the sequence is \( 4 \).