well...if you notice, the first value is -21, the second is -27... what happened? it went "down" by 6 units...ok... the next one is -33, wait a second? it went down again by 6 units? -27 - 6 = -33, the next is -39, again 6 units, what the dickens?
well, you get the next term by simply subtracting 6 or "adding" -6 to the current one, thus is an arithmetic sequence, so thus -6 is then the "common difference", and the first value is -27.
[tex]\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
a_1=-27\\
d=-6\\
n=23
\end{cases}
\\\\\\
a_n=-27+(23-1)(-6)\implies a_{23}=-27+(23-1)(-6)
\\\\\\
a_{23}=-27+(-132)\implies a_{23}=-27-132\implies \boxed{a_{23}=-159}[/tex]
