\(\text{www.the}\beta\text{etafunction.com}\)
Home
Login
Questions: Algebra BusinessCalculus
Please login to create an exam or a quiz.
Find the general term of the sequence \(\displaystyle 4,- \frac{44}{15},\frac{484}{225},\ldots\)
The common ratio is \(\displaystyle r=\frac{a_2}{a_1}=- \frac{11}{15}\). Using the first term and the common ratio gives \(\displaystyle a_n=4\left( - \frac{11}{15} \right)^{n-1}\)
\begin{question}Find the general term of the sequence $4,- \frac{44}{15},\frac{484}{225},\ldots$
\soln{9cm}{The common ratio is $r=\frac{a_2}{a_1}=- \frac{11}{15}$. Using the first term and the common ratio gives $a_n=4\left( - \frac{11}{15} \right)^{n-1}$}
\end{question}
\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage[margin=2cm]{geometry}
\usepackage{tcolorbox}
\newcounter{ExamNumber}
\newcounter{questioncount}
\stepcounter{questioncount}
\newenvironment{question}{{\noindent\bfseries Question \arabic{questioncount}.}}{\stepcounter{questioncount}}
\renewcommand{\labelenumi}{{\bfseries (\alph{enumi})}}
\newif\ifShowSolution
\newcommand{\soln}[2]{%
\ifShowSolution%
\noindent\begin{tcolorbox}[colframe=blue,title=Solution]#2\end{tcolorbox}\else%
\vspace{#1}%
\fi%
}%
\newcommand{\hideifShowSolution}[1]{%
\ifShowSolution%
%
\else%
#1%
\fi%
}%
\everymath{\displaystyle}
\ShowSolutiontrue
\begin{document}\begin{question}(10pts) The question goes here!
\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>Find the general term of the sequence <img class="equation_image" title=" \displaystyle 4,- \frac{44}{15},\frac{484}{225},\ldots " src="/equation_images/%20%5Cdisplaystyle%204%2C-%20%5Cfrac%7B44%7D%7B15%7D%2C%5Cfrac%7B484%7D%7B225%7D%2C%5Cldots%20" alt="LaTeX: \displaystyle 4,- \frac{44}{15},\frac{484}{225},\ldots " data-equation-content=" \displaystyle 4,- \frac{44}{15},\frac{484}{225},\ldots " /> </p> </p><p> <p>The common ratio is <img class="equation_image" title=" \displaystyle r=\frac{a_2}{a_1}=- \frac{11}{15} " src="/equation_images/%20%5Cdisplaystyle%20r%3D%5Cfrac%7Ba_2%7D%7Ba_1%7D%3D-%20%5Cfrac%7B11%7D%7B15%7D%20" alt="LaTeX: \displaystyle r=\frac{a_2}{a_1}=- \frac{11}{15} " data-equation-content=" \displaystyle r=\frac{a_2}{a_1}=- \frac{11}{15} " /> . Using the first term and the common ratio gives <img class="equation_image" title=" \displaystyle a_n=4\left( - \frac{11}{15} \right)^{n-1} " src="/equation_images/%20%5Cdisplaystyle%20a_n%3D4%5Cleft%28%20-%20%5Cfrac%7B11%7D%7B15%7D%20%5Cright%29%5E%7Bn-1%7D%20" alt="LaTeX: \displaystyle a_n=4\left( - \frac{11}{15} \right)^{n-1} " data-equation-content=" \displaystyle a_n=4\left( - \frac{11}{15} \right)^{n-1} " /> </p> </p>