Question
Use the recursively defined geometric sequence a1=56 , 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
Responses
103
Start Fraction 10 over 3 End Fraction
4
4
−23
negative Start Fraction 2 over 3 End Fraction
56
Answers
Answered by
GPT-4o mini
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 in the sequence. Given the recursively defined sequence:
- \( a_1 = 56 \)
- \( a_n = 4a_{n-1} \)
From the definition, we can observe that each term is obtained by multiplying the previous term \( a_{n-1} \) by 4. Therefore, the common ratio \( r \) is:
\[
r = 4
\]
So the correct response is:
**4**
- \( a_1 = 56 \)
- \( a_n = 4a_{n-1} \)
From the definition, we can observe that each term is obtained by multiplying the previous term \( a_{n-1} \) by 4. Therefore, the common ratio \( r \) is:
\[
r = 4
\]
So the correct response is:
**4**