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\lhead{Mathematics and Digital Art}
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\rhead{10 November 2017}
\lfoot{Matsko}
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%\rfoot{12 September 2016}

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All answers should be fractions, not decimals.  Be sure to use the formulas we learned in class -- don't just add the numbers!
\begin{enumerate}
\item Find the $4^{\rm th}$ term in the geometric sequence $5, -3\ldots.$
\vskip 2.1in

%\item Compute. $\displaystyle\sum_{i=1}^{6}2(-3)^i.$
%\vskip 1.6in

\item Compute $\displaystyle\sum_{k=0}^5\dfrac{(-3)^k}{2^{k+1}}.$
\vskip 2.1in

\item You are given a geometric sequence with $a=2$ and $r=-\dfrac13.$  For what $n$ does $S_n=\dfrac{122}{81}$?
\vskip 2.1in

\eject

\item Compute $\displaystyle\sum_{n=0}^\infty\dfrac{7^n}{4^{2n}}.$
\vskip 2.1in

\item Suppose that five terms of a geometric sequence with ratio $r=-\dfrac23$ sum to $\dfrac{55}{9}.$  What is the first term of the sequence?
\vskip 2.1in

\item Suppose an infinite geometric series has ratio $-\dfrac35$ and sums to $4$.  What is the first term for this series?
\vskip 2.1in

\end{enumerate}
\eject
\end{document}
Answers:
\begin{enumerate}
\item $-\dfrac{81}{64}.$
\item $1092.$
\item $\dfrac{25}{1024}.$
\item $n=6.$
\item $\dfrac54.$
\item $4.$
\item $\dfrac74.$
\item Answers will vary!
\end{enumerate}


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