Given the recursive formula for the geometric sequence a1=5

Question

, an=25an−1
, find the second term of the sequence.(1 point
Responses

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
a subscript 2 baseline equals 2

a2=85

Answer 1

To find the second term \( a_2 \) of the geometric sequence defined by the recursive formula \( a_1 = 5 \) and \( a_n = 25 a_{n-1} \), we can calculate it as follows:

1. We know that \( a_1 = 5 \).
2. Using the recursive formula for \( n = 2 \):

\[ a_2 = 25 \cdot a_1 \]

Substituting \( a_1 \):

\[ a_2 = 25 \cdot 5 = 125 \]

None of the provided response options include \( a_2 = 125 \). It appears that there may be an error in the options listed.

However, according to the recursive definition, the second term \( a_2 \) is indeed \( 125 \).