Use the recursively defined geometric sequence a1=5/6

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

4
4

10/3
Start Fraction 10 over 3 End Fraction

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

5/6

1 answer

In a geometric sequence, each term is obtained by multiplying the previous term by a constant factor called the common ratio.

In the given recursive definition of the sequence:

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

From the recursive relation, we can see that each term is obtained by multiplying the previous term by 4. Therefore, the common ratio \( r \) is:

\[ r = 4 \]

Thus, the common ratio of the geometric sequence is 4.