Answer:
[tex]\huge\boxed{a_n=\dfrac{3}{5}\cdot5^n}[/tex]
Step-by-step explanation:
[tex]a_1=3\\\\a_2=15=5\cdot3=5a_1\\\\a_3=75=5\cdot15=5a_2\\\\a_4=375=5\cdot75=5a_3\\\vdots\\\\\text{It's a geometric series with first term}\ a_1=3\ \text{and the common ratio}\ r=5.\\\\\text{The explicit formula of a geometric sequence:}\\\\a_n=a_1r^{n-1}\\\\\text{Substitute:}\\\\a_n=3\cdot5^{n-1}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\a_n=3\cdot5^{n+(-1)}\\\\a_n=3\cdot5^n\cdot5^{-1}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\a_n=3\cdot5^n\cdot\dfrac{1}{5}\\\\\text{Finally:}\\\\a_n=\dfrac{3}{5}\cdot5^n[/tex]
