\begin{enumerate}
\item Si $u_0=5$ et $r=3$, calculer $u_0+u_1+\cdots+u_{100}$.

\suite{u}{n}{} est une suite arithmétique donc :
\[
u_0+u_1+\cdots+u_n=\dfrac{u_0+u_n}{2}\times(n+1)
\]
donc ici :
\begin{align*}
u_0+u_1+\cdots+u_{100} & = \dfrac{5+(5+100\times3)}{2}\times101\\
& = 155\times101\\
\Aboxed{u_0+u_1+\cdots+u_{100} & = \numprint{15655}}
\end{align*}

\item Si $u_0=3$ et $u_{50}=60$, calculer $u_0+u_1+\cdots+u_{50}$.

\begin{align*}
u_0+u_1+\cdots+u_{50} & = \dfrac{3+60}{2}\times51\\
& = 155\times101\\
\Aboxed{u_0+u_1+\cdots+u_{100} & = \numprint{1606,5}}
\end{align*}

\newpage
\item Si $u_1=60$ et $r=5$, calculer $u_1+u_2+\cdots+u_{100}$.

\begin{align*}
u_1+u_2+\cdots+u_{100} & = \dfrac{u_1+u_{100}}{2}\times100\\
& = \dfrac{60+(60+5\times99)}{2}\times100\\
& = \dfrac{\numprint{61500}}{2}\\
\Aboxed{u_1+u_2+\cdots+u_{100} & = \numprint{30750}}
\end{align*}

\item Si $u_1=50$ et $u_{50}=1$, calculer $u_1+u_2+\cdots+u_{50}$.

\begin{align*}
u_1+u_2+\cdots+u_{50} & = \dfrac{u_1+u_{50}}{2}\times50\\
& \dfrac{50+1}{2}\\
\Aboxed{u_1+u_2+\cdots+u_{50} & = 25,5}
\end{align*}
\end{enumerate}