Can someone please check my answer

Answer:
See below
Step-by-step explanation:
your answer for [tex]a_{1}[/tex] is correct, but I get
[tex]a_{n} = \frac{2}{25} 5^{n}[/tex] for the second answer
[tex]\frac{2}{5} 5^{n - 1} = \frac{2}{5} 5^{n} 5^{-1} = \frac{2}{5} 5^{n} \frac{1}{5}[/tex]
[tex]a_{n} = \frac{2}{25} 5^{n}[/tex]