Question

What number comes next in the sequence?16, 8, 4, 2, 1, ?01/2 1-1-2

Answer 1

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

`r=(a_2)/(a_1)=(8)/(16)=(1)/(2)`

Now

`a_n=a_1r^(n-1)`

`\begin{gathered} n=6 \\ a_1=16 \\ r=(1)/(2) \\ \\ a_6=16*(1)/(2)^((6-1)) \\ \\ a_6=16*(1)/(2)^((5)) \\ \\ a_6=16*(1)/(32) \\ \\ a_6=(16)/(32)=(1)/(2) \end{gathered}`

The final answer

`(1)/(2)`