Answered

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

Sagot :

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]

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