find the sum of the first 100 term of the geometric series with the first term 5 and the common ratio is -2

find the sum of the first 100 term of the geometric series with the first term 5 and the common ratio is -2

$$\\\small{
\begin{array}{rccl}
s_{100} &=& \textcolor[rgb]{1,0,0}{5}+&5(-2)^1+5(-2)^2+5(-2)^3+5(-2)^4+\dots+5(-2)^{98}+5(-2)^{99}
}\\\\
(-2)s_{100}&=& & 5(-2)^1+5(-2)^2+5(-2)^3+5(-2)^4+\dots+5(-2)^{98}+5(-2)^{99}+\textcolor[rgb]{1,0,0}{5(-2)^{100}}
}\\\\
\hline
s_{100}-(-2)s_{100}&=& 5-&5(-2)^{100}\\\\
s_{100}+2s_{100}&=& 5-&5(-2)^{100}\\\\
3s_{100}&=& 5-&5(-2)^{100}\\\\
\end{array}
}\\\\
\small
\begin{array}{rcl}
s_{100} &=& \dfrac{ 5-5(-2)^{100} } {3}\\\\
s_{100} &=& -2112751000380382335827838675625
\end{array}
}$$