The explicit rule for a sequence is given.
an= 2/5 (5)^n−1

Step-by-step explanation:
A geometric series is:
an = a₁ (r)^(n-1)
Here:
an = 2/5 (5)^(n-1)
So a₁ = 2/5, and r = 5. So an = 5an-1.
Your answer is correct, well done!