Arithmetic and Geometric Sequences as Functions Practice Test

The sequence is defined recursively by $a_1=6$ and $a_{n+1}=\tfrac{1}{2}a_n$. Write the explicit formula for $a_n$ (domain: positive integers).

A student deposits $\$40$ into a jar each week and does not remove any money. Let $a_n$ be the total amount in the jar after $n$ weeks, with $a_1=40$. Write both recursive and explicit formulas (domain: positive integers).