Question
Given the recursive formula for the geometric sequence a₁ = 5, an = an-1, find the second term of the sequence.
a_{2} = 2
a_{2} = 8/5
a_{2} = 5 2/5
a_{2} = 2/5
a_{2} = 2
a_{2} = 8/5
a_{2} = 5 2/5
a_{2} = 2/5
Answers
GPT-4o mini
The recursive formula provided for the geometric sequence is \( a_n = a_{n-1} \cdot r \), where \( r \) is the common ratio.
You've given that the first term \( a_1 = 5 \). However, to find the second term \( a_2 \), we need the value of the common ratio \( r \).
In the context of the information provided, if \( a_n = a_{n-1} \), it implies that \( r = 1 \) (since the ratio between consecutive terms is the same).
Given \( r = 1 \):
\[
a_2 = a_1 \cdot r = 5 \cdot 1 = 5
\]
Thus, the second term \( a_2 = 5 \).
Among the options provided, the correct answer is:
**None of the options match**, but the correct value for \( a_2 \) based on the reasoning is **5**.
If you're looking for a specific common ratio or if there's information missing regarding the common ratio, please provide that, and I can help further.
You've given that the first term \( a_1 = 5 \). However, to find the second term \( a_2 \), we need the value of the common ratio \( r \).
In the context of the information provided, if \( a_n = a_{n-1} \), it implies that \( r = 1 \) (since the ratio between consecutive terms is the same).
Given \( r = 1 \):
\[
a_2 = a_1 \cdot r = 5 \cdot 1 = 5
\]
Thus, the second term \( a_2 = 5 \).
Among the options provided, the correct answer is:
**None of the options match**, but the correct value for \( a_2 \) based on the reasoning is **5**.
If you're looking for a specific common ratio or if there's information missing regarding the common ratio, please provide that, and I can help further.