Given the recursive formula for the geometric sequence a^1=5a^n=2/5a^n-1 find the second term of the sequence.(1 point)

Question

Responses

a2=8/5

a2=2/5

a2=2

a2=5 2/5

Answer 1

To find the second term of the geometric sequence given the recursive formula \( a^1 = 5 \) and \( a^n = \frac{2}{5} a^{n-1} \), we start by calculating the second term \( a^2 \).

1. We know \( a^1 = 5 \).
2. Using the recursive formula for \( n = 2 \): \[ a^2 = \frac{2}{5} a^{1} \] Substituting \( a^1 = 5 \) into the equation: \[ a^2 = \frac{2}{5} \cdot 5 \] Simplifying: \[ a^2 = \frac{2 \cdot 5}{5} = 2 \]

Thus, the second term of the sequence is \( a^2 = 2 \).

The correct response is:

a2=2