Answer:
[tex]\large\boxed{a(n)=16\left(\dfrac{1}{2}\right)^{n-1}}[/tex]
Step-by-step explanation:
[tex]a(1)=16\\\\a(2)=16:2=8\\\\a(3)=8:2=4\\\\a(4)=4:2=2\\\\a(5)=2:2=1\\\\a(n)=a_{n-1}:2=\dfrac{1}{2}a_{n-1}[/tex]
This is a geometric series with the common ratio [tex]r=\dfrac{1}{2}[/tex] and the first term [tex]a_1=16[/tex].
An explicit formula of the n-th term of a geometric sequence:
[tex]a_n=a_1r^{n-1}[/tex]
Substitute:
[tex]a_n=16\left(\dfrac{1}{2}\right)^{n-1}[/tex]
