Question

Question

Given the recursive formula for the geometric sequence a1=5
, an=25an−1
, 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

Answer 1

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 \( a_2 = 125 \).