Question

Use the recursively defined geometric sequence a1=56
𝑎
1
=
5
6
, an=4an−1
𝑎
𝑛
=
4
𝑎
𝑛
−
1
and find the common ratio.(1 point)
Responses

56
5
6
Start Fraction 5 over 6 End Fraction

−23
−
2
3
negative Start Fraction 2 over 3 End Fraction

4
4

103

Answer 1

In a geometric sequence, the common ratio \( r \) is defined as the factor by which we multiply each term to get to the next term.

Given the recursively defined geometric sequence:

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

We can see that each term is generated by multiplying the previous term \( a_{n-1} \) by \( 4 \).

This means that the common ratio \( r \) is:

\[
r = 4
\]

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

So the correct response is **4**.