10, 14, 18 ....

notice, we get the next term by simply adding 4 to the current term, thus "4" is the "common difference, and we know that 10 is the first term.

$\bf n^{th}\textit{ term of an arithmetic sequence}
\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
a_1=10\\
d=4\\
n=17
\end{cases}
\\\\\\
a_{17}=10+(17-1)(4)\implies a_{17}=10+(16)(4)
\\\\\\
a_{17}=10+64\implies a_{17}=74\\\\
-------------------------------$

$\bf \textit{ sum of a finite arithmetic sequence}
\\\\
S_n=\cfrac{n(a_1+a_n)}{2}\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
----------\\
a_1=10\\
a_{17}=74\\
n=17
\end{cases}
\\\\\\
S_{17}=\cfrac{17(10+74)}{2}\implies S_{17}=\cfrac{17(84)}{2}\implies S_{17}=714$

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