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Questions: Algebra BusinessCalculus
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Use \(\displaystyle a_1=-6\) and \(\displaystyle a_2=-2\) and \(\displaystyle a_n=5a_{n-1} -9a_{n-2}\) to find \(\displaystyle a_{6}\)
Finding the next term in the sequence gives \(\displaystyle a_3=(5)(-6)+(-9)(-2)=-12\)
\(\displaystyle a_{4}=(5)(-2)+(-9)(-12)=98\).
\(\displaystyle a_{5}=(5)(-12)+(-9)(98)=-942\).
\(\displaystyle a_{6}=(5)(98)+(-9)(-942)=8968\).
\begin{question}Use $a_1=-6$ and $a_2=-2$ and $a_n=5a_{n-1} -9a_{n-2}$ to find $a_{6}$
\soln{9cm}{Finding the next term in the sequence gives $a_3=(5)(-6)+(-9)(-2)=-12$\newline
$a_{4}=(5)(-2)+(-9)(-12)=98$. \newline
$a_{5}=(5)(-12)+(-9)(98)=-942$. \newline
$a_{6}=(5)(98)+(-9)(-942)=8968$. \newline
}
\end{question}
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\begin{document}\begin{question}(10pts) The question goes here!
\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>Use <img class="equation_image" title=" \displaystyle a_1=-6 " src="/equation_images/%20%5Cdisplaystyle%20a_1%3D-6%20" alt="LaTeX: \displaystyle a_1=-6 " data-equation-content=" \displaystyle a_1=-6 " /> and <img class="equation_image" title=" \displaystyle a_2=-2 " src="/equation_images/%20%5Cdisplaystyle%20a_2%3D-2%20" alt="LaTeX: \displaystyle a_2=-2 " data-equation-content=" \displaystyle a_2=-2 " /> and <img class="equation_image" title=" \displaystyle a_n=5a_{n-1} -9a_{n-2} " src="/equation_images/%20%5Cdisplaystyle%20a_n%3D5a_%7Bn-1%7D%20-9a_%7Bn-2%7D%20" alt="LaTeX: \displaystyle a_n=5a_{n-1} -9a_{n-2} " data-equation-content=" \displaystyle a_n=5a_{n-1} -9a_{n-2} " /> to find <img class="equation_image" title=" \displaystyle a_{6} " src="/equation_images/%20%5Cdisplaystyle%20a_%7B6%7D%20" alt="LaTeX: \displaystyle a_{6} " data-equation-content=" \displaystyle a_{6} " /> </p> </p><p> <p>Finding the next term in the sequence gives <img class="equation_image" title=" \displaystyle a_3=(5)(-6)+(-9)(-2)=-12 " src="/equation_images/%20%5Cdisplaystyle%20a_3%3D%285%29%28-6%29%2B%28-9%29%28-2%29%3D-12%20" alt="LaTeX: \displaystyle a_3=(5)(-6)+(-9)(-2)=-12 " data-equation-content=" \displaystyle a_3=(5)(-6)+(-9)(-2)=-12 " /> <br>
<img class="equation_image" title=" \displaystyle a_{4}=(5)(-2)+(-9)(-12)=98 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B4%7D%3D%285%29%28-2%29%2B%28-9%29%28-12%29%3D98%20" alt="LaTeX: \displaystyle a_{4}=(5)(-2)+(-9)(-12)=98 " data-equation-content=" \displaystyle a_{4}=(5)(-2)+(-9)(-12)=98 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{5}=(5)(-12)+(-9)(98)=-942 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B5%7D%3D%285%29%28-12%29%2B%28-9%29%2898%29%3D-942%20" alt="LaTeX: \displaystyle a_{5}=(5)(-12)+(-9)(98)=-942 " data-equation-content=" \displaystyle a_{5}=(5)(-12)+(-9)(98)=-942 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{6}=(5)(98)+(-9)(-942)=8968 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B6%7D%3D%285%29%2898%29%2B%28-9%29%28-942%29%3D8968%20" alt="LaTeX: \displaystyle a_{6}=(5)(98)+(-9)(-942)=8968 " data-equation-content=" \displaystyle a_{6}=(5)(98)+(-9)(-942)=8968 " /> . <br>
</p> </p>