Find the next three terms of each arithmetic sequence.

$16,4,-8,-20,\mathrm{...}$

The given arithmetic sequence is: $16,4,-8,-20$.

From the given arithmetic sequence, it can be noticed that the first, second, third, and fourth terms of the arithmetic sequence are $16,4,-8$and $-20$respectively.

The common difference of the arithmetic sequence is the difference between the succeeding term and its preceding term.

Therefore, the common difference$\left(d\right)$ of the given arithmetic sequence is:

$$\begin{gathered} d=4-16 \\ =-12 \end{gathered}$$

Therefore, the first term and the common difference of the given arithmetic sequence are 16 and$-12$ respectively.

The $n\mathrm{th}$term $\left(a_n\right)$of the given arithmetic sequence is given by:

$a_n=a_1+\left(n-1\right)d$, where $a_1$is the first term and $d$is a common difference.

The next three terms of the given arithmetic sequence are fifth, sixth, and seventh terms.

Therefore, the next three terms of the given arithmetic sequence having $a_1=16$and $d=-12$are:

$a_5=a_1+\left(5-1\right)d$

$$\begin{gathered} =16+\left(4\right)\left(-12\right) \\ =16-48 \\ =-32 \end{gathered}$$

$a_6=a_1+\left(6-1\right)d$

$$\begin{gathered} =16+\left(5\right)\left(-12\right) \\ =16-60 \\ =-44 \end{gathered}$$

$a_7=a_1+\left(7-1\right)d$

$$\begin{gathered} =16+\left(6\right)\left(-12\right) \\ =16-72 \\ =-56 \end{gathered}$$

Therefore, the next three terms of the given arithmetic sequence are $-32,-44$ and $-56$.