\documentclass[a4paper,10pt]{article}

\usepackage[Mickael]{ammaths}
\usepackage{alterqcm}

\begin{document}

\entete{European section, season 2}{Arithmetic sequences}{Test}

\begin{center}
\begin{minipage}{12cm}
{\sf Some items of this test are multiple choice questions. They are all worth 1 point each. Other items are free
response questions, all of them worth 2 points, where any incomplete or imperfect answer will be rewarded.}
\end{minipage}
\end{center}



\begin{alterqcm}[tone=\sf QUESTIONS,ttwo=\sf ANSWERS,symb=\dingsquare,corsymb=\dingchecksquare]
\AQquestion{If the numbers $16$ and $8$ are consecutive terms in an arithmetic sequence (in that order), what is the next term ?}{%
 {$16$},
 {$0$},
 {$4$},
 {$-8$}	}
\AQquestion{Consider the arithmetic sequence $(\frac{11}{3},\frac{8}{3},\frac{5}{3},\frac{2}{3},\ldots)$. The common difference in this sequence is }{%
 {$\frac{11}{3}$},
 {$-1$},
 {$1$},
 {$-\frac{1}{3}$}	}
\AQquestion{Consider the arithmetic sequence whose common difference is $5$ and first term is $8$. Then the tenth term is}{%
 {$53$},
 {$58$},
 {$85$},
 {$77$}	}
\AQquestion{Consider the arithmetic sequence $(a_n)$ such that $a_1=17$ and $a_3=23$. The common difference in this sequence is}{%
 {$6$},
 {$-3$},
 {$3$},
 {$17$}	}
\AQquestion{Consider the arithmetic sequence $(a_n)$ such that $a_2=117$ and $a_{12}=187$. The common difference in this sequence is}{%
 {$70$},
 {$-7$},
 {$\frac{70}{9}$},
 {$7$}}
\end{alterqcm}

\begin{enumerate}\setcounter{enumi}{5}
\item Let $(a_n)$ be an arithmetic sequence of first term $a_1$ and common difference $d$.
	\begin{enumerate}
	\item Write any term $a_{n+1}$ as a function of the previous term.
	\begin{center}
	\fbox{\parbox{5cm}{\rule{0pt}{20pt}}}	
	\end{center}
	\item Write any term $a_{n}$ as a function of the first term and the common difference.
	\begin{center}
	\fbox{\parbox{5cm}{\rule{0pt}{20pt}}}	
	\end{center}
	\item Let $a_n$ and $a_m$ be two terms  in the sequence. Write down the relation between these two terms, using the common difference.
	\begin{center}
	\fbox{\parbox{5cm}{\rule{0pt}{20pt}}}	
	\end{center}
	\end{enumerate}
\end{enumerate}

\pagebreak

\begin{alterqcm}[tone=\sf QUESTIONS,ttwo=\sf ANSWERS,symb=\dingsquare,corsymb=\dingchecksquare,numbreak=6]
\AQquestion{The sum of the $n$ first terms of an arithmetic sequence $(a_n)$ is given by the formula}{%
 {$\dis\frac{a_1+a_n}{2}$},
 {$\dis(n+1)\frac{a_1+a_n}{2}$},
 {$\dis n\times\frac{a_1+a_n}{2}$},
 {$\dis a_1\times\frac{1+n}{2}$}	}
\AQquestion{The sum of the $5$ first terms of an arithmetic sequence of first term $3$ and common difference $0.5$ is equal to }{%
 {$20$},
 {$1.75$},
 {$8$},
 {$25.5$}	}
\AQquestion{Consider an arithmetic sequence such that its first term is $a_1=-15$ and $a_{100}=18$. The sum of its one hundred first terms is}{%
 {$1.5$},
 {$18$},
 {$150$},
 {$-270$}	}
\AQquestion{The common difference of the previous sequence is }{%
 {$\frac{1}{3}$},
 {$-\frac{1}{3}$},
 {$33$},
 {$99$}	}
\end{alterqcm}

\begin{center}

\end{center}

\emph{Please answer these last two questions on a separate paper, with your name on it.}

\begin{enumerate}\setcounter{enumi}{10}
\item Divide 138 hekats of barley among 8 men so that the common difference is 3/2 hekats of barley.
\item A polygon has 25 sides, the lengths of which form an
arithmetic sequence. If the polygon has a perimeter of 1 100 cm, and
the longest side is ten times the shortest side, find the lengths of
the shortest and longest sides.
\end{enumerate}


\end{document}
