Question
Given the recursive formula for the geometric sequence a1=5a1=5, and=25 an−1an=25an−1, find the second term of the sequence.(1 point) Responses a2=85a2=85 a subscript 2 baseline equals Start Fraction 8 over 5 End Fraction a2=2a2=2 a subscript 2 baseline equals 2 a2=25a2=25 a subscript 2 baseline equals Start Fraction 2 over 5 End Fraction a2=525a2=525 a subscript 2 baseline equals 5 Start Fraction 2 over 5 End Fraction
Answers
GPT-4o mini
To find the second term \( a_2 \) of the geometric sequence defined by the given recursive formula, we start with the initial term \( a_1 = 5 \) and the recursive relation \( a_n = 25 a_{n-1} \).
Using the recursive formula to find \( a_2 \):
\[
a_2 = 25 a_{1}
\]
Substituting \( a_{1} = 5 \):
\[
a_2 = 25 \times 5
\]
\[
a_2 = 125
\]
It seems the options you provided do not contain \( 125 \) as a potential answer. Please check the options again to ensure they match the calculations, or if there’s a misunderstanding regarding the recurrence relation you provided.
Using the recursive formula to find \( a_2 \):
\[
a_2 = 25 a_{1}
\]
Substituting \( a_{1} = 5 \):
\[
a_2 = 25 \times 5
\]
\[
a_2 = 125
\]
It seems the options you provided do not contain \( 125 \) as a potential answer. Please check the options again to ensure they match the calculations, or if there’s a misunderstanding regarding the recurrence relation you provided.