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=2
a subscript 2 baseline equals 2

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

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 \( a_2 \):

1. **Identify the first term**:
\[
a_1 = 5
\]

2. **Use the recursive formula to find the second term \( a_2 \)**:
\[
a_2 = 25a_1
\]
Substituting \( a_1 \):
\[
a_2 = 25 \times 5 = 125
\]

Now looking at the provided options, the correct answer for \( a_2 \) is not in the list. The value \( a_2 = 125 \) can be further analyzed but does not match any of the provided response options.

Thus, based on the calculation, \( a_2 = 125 \).