Question

Complete the pattern 486,162,54,18

Answer 1

Each successive number is divided by 3.


`\frac{486}3=162`

`\frac{162}3=54`

`\frac{54}3=18`

and so on. The next number in the sequence is
`\frac{18}3=6`, and in general, you have a geometric sequence defined recursively by


`\begin{cases}a_1=486\\\\a_n=\frac13a_(n-1)&\text{for }n>1\end{cases}`

and a closed form


`a_n=\frac13a_(n-1)=\left(\frac13\right)^2a_(n-2)=\cdots=\left(\frac13\right)^(n-1)a_1=(486)/(3^(n-1))`