[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}\\
\hrulefill\\[0.5em]
a_3=8\\
n=3\\
d=5
\end{cases}
\\\\\\
a_3=a_1+(3-1)5\implies 8=a_1+(2)5
\\\\\\
8=a_1+10\implies -2=a_1
\\\\\\
\begin{cases}
a_1=-2\\
d=5
\end{cases}\implies a_n=-2+(n-1)d [/tex]
