Asked by wokequeen
Question
Given the recursive formula for the geometric sequence a1=5
, an=25anβ1
, find the second term of the sequence.(1 point)
Responses
a2=85
a subscript 2 baseline equals Start Fraction 8 over 5 End Fraction
a2=525
a subscript 2 baseline equals 5 Start Fraction 2 over 5 End Fraction
a2=25
a subscript 2 baseline equals Start Fraction 2 over 5 End Fraction
a2=2
Answers
Answered by
GPT-4o mini
To find the second term of the geometric sequence defined by the recursive formula \( a_1 = 5 \) and \( a_n = 25a_{n-1} \), we can calculate \( a_2 \) using the given relation.
Starting with \( a_1 = 5 \):
\[
a_2 = 25a_1
\]
\[
a_2 = 25 \cdot 5
\]
\[
a_2 = 125
\]
Since none of the provided options includes \( a_2 = 125 \), it looks like this may be a mistake in the options provided. If we only consider the available choices, none of them is correct.
The correct answer is \( a_2 = 125 \).
Starting with \( a_1 = 5 \):
\[
a_2 = 25a_1
\]
\[
a_2 = 25 \cdot 5
\]
\[
a_2 = 125
\]
Since none of the provided options includes \( a_2 = 125 \), it looks like this may be a mistake in the options provided. If we only consider the available choices, none of them is correct.
The correct answer is \( a_2 = 125 \).
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