Answer :
Given
What number comes next in the sequence?
16, 8, 4, 2, 1, ?
Solution
This is a Geometric sequence, we need to find the common ratio
The formula for the common ratio is
[tex]r=\frac{a_2}{a_1}=\frac{8}{16}=\frac{1}{2}[/tex]Now
[tex]a_n=a_1r^{n-1}[/tex][tex]\begin{gathered} n=6 \\ a_1=16 \\ r=\frac{1}{2} \\ \\ a_6=16\times\frac{1}{2}^{(6-1)} \\ \\ a_6=16\times\frac{1}{2}^{(5)} \\ \\ a_6=16\times\frac{1}{32} \\ \\ a_6=\frac{16}{32}=\frac{1}{2} \end{gathered}[/tex]The final answer
[tex]\frac{1}{2}[/tex]