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 $a_n=25a_{n-1}$, 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 $125$.