so hmmm 7, 0, -7.... what the dickens is going on? hmmm is really dropping each time by 7, so, 7-7, 0, and 0-7, -7 and so on.
so, the "common difference" is then -7, and our first term is 7, now, who's -175? let's check.
[tex]\bf 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}\\
----------\\
d=-7\\
a_1=7\\
a_n=-175
\end{cases}
\\\\\\
-175=7+(n-1)(-7)\implies -175=7+7-7n
\\\\\\
7n=14+175\implies 7n=189\implies n=\cfrac{189}{7}\implies n=\stackrel{terms}{27}[/tex]
