Respuesta :

LammettHash
Each successive number is divided by 3.

[tex]\dfrac{486}3=162[/tex]
[tex]\dfrac{162}3=54[/tex]
[tex]\dfrac{54}3=18[/tex]

and so on. The next number in the sequence is [tex]\dfrac{18}3=6[/tex], and in general, you have a geometric sequence defined recursively by

[tex]\begin{cases}a_1=486\\\\a_n=\dfrac13a_{n-1}&\text{for }n>1\end{cases}[/tex]

and a closed form

[tex]a_n=\dfrac13a_{n-1}=\left(\dfrac13\right)^2a_{n-2}=\cdots=\left(\dfrac13\right)^{n-1}a_1=\dfrac{486}{3^{n-1}}[/tex]

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