\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.
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\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}