Question

Complete the pattern 486,162,54,18

Answer 1

Each successive number is divided by 3.

$\dfrac{486}3=162$
$\dfrac{162}3=54$
$\dfrac{54}3=18$

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

$\begin{cases}a_1=486\\\\a_n=\dfrac13a_{n-1}&\text{for }n>1\end{cases}$

and a closed form

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