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Questions: Algebra BusinessCalculus
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Use \(\displaystyle a_1=-6\) and \(\displaystyle a_2=2\) and \(\displaystyle a_n=-6a_{n-1} -4a_{n-2}\) to find \(\displaystyle a_{9}\)
Finding the next term in the sequence gives \(\displaystyle a_3=(-6)(-6)+(-4)(2)=28\)
\(\displaystyle a_{4}=(-6)(2)+(-4)(28)=-124\).
\(\displaystyle a_{5}=(-6)(28)+(-4)(-124)=328\).
\(\displaystyle a_{6}=(-6)(-124)+(-4)(328)=-568\).
\(\displaystyle a_{7}=(-6)(328)+(-4)(-568)=304\).
\(\displaystyle a_{8}=(-6)(-568)+(-4)(304)=2192\).
\(\displaystyle a_{9}=(-6)(304)+(-4)(2192)=-10592\).
\begin{question}Use $a_1=-6$ and $a_2=2$ and $a_n=-6a_{n-1} -4a_{n-2}$ to find $a_{9}$
\soln{9cm}{Finding the next term in the sequence gives $a_3=(-6)(-6)+(-4)(2)=28$\newline
$a_{4}=(-6)(2)+(-4)(28)=-124$. \newline
$a_{5}=(-6)(28)+(-4)(-124)=328$. \newline
$a_{6}=(-6)(-124)+(-4)(328)=-568$. \newline
$a_{7}=(-6)(328)+(-4)(-568)=304$. \newline
$a_{8}=(-6)(-568)+(-4)(304)=2192$. \newline
$a_{9}=(-6)(304)+(-4)(2192)=-10592$. \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%3D2%20" alt="LaTeX: \displaystyle a_2=2 " data-equation-content=" \displaystyle a_2=2 " /> and <img class="equation_image" title=" \displaystyle a_n=-6a_{n-1} -4a_{n-2} " src="/equation_images/%20%5Cdisplaystyle%20a_n%3D-6a_%7Bn-1%7D%20-4a_%7Bn-2%7D%20" alt="LaTeX: \displaystyle a_n=-6a_{n-1} -4a_{n-2} " data-equation-content=" \displaystyle a_n=-6a_{n-1} -4a_{n-2} " /> to find <img class="equation_image" title=" \displaystyle a_{9} " src="/equation_images/%20%5Cdisplaystyle%20a_%7B9%7D%20" alt="LaTeX: \displaystyle a_{9} " data-equation-content=" \displaystyle a_{9} " /> </p> </p><p> <p>Finding the next term in the sequence gives <img class="equation_image" title=" \displaystyle a_3=(-6)(-6)+(-4)(2)=28 " src="/equation_images/%20%5Cdisplaystyle%20a_3%3D%28-6%29%28-6%29%2B%28-4%29%282%29%3D28%20" alt="LaTeX: \displaystyle a_3=(-6)(-6)+(-4)(2)=28 " data-equation-content=" \displaystyle a_3=(-6)(-6)+(-4)(2)=28 " /> <br>
<img class="equation_image" title=" \displaystyle a_{4}=(-6)(2)+(-4)(28)=-124 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B4%7D%3D%28-6%29%282%29%2B%28-4%29%2828%29%3D-124%20" alt="LaTeX: \displaystyle a_{4}=(-6)(2)+(-4)(28)=-124 " data-equation-content=" \displaystyle a_{4}=(-6)(2)+(-4)(28)=-124 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{5}=(-6)(28)+(-4)(-124)=328 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B5%7D%3D%28-6%29%2828%29%2B%28-4%29%28-124%29%3D328%20" alt="LaTeX: \displaystyle a_{5}=(-6)(28)+(-4)(-124)=328 " data-equation-content=" \displaystyle a_{5}=(-6)(28)+(-4)(-124)=328 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{6}=(-6)(-124)+(-4)(328)=-568 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B6%7D%3D%28-6%29%28-124%29%2B%28-4%29%28328%29%3D-568%20" alt="LaTeX: \displaystyle a_{6}=(-6)(-124)+(-4)(328)=-568 " data-equation-content=" \displaystyle a_{6}=(-6)(-124)+(-4)(328)=-568 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{7}=(-6)(328)+(-4)(-568)=304 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B7%7D%3D%28-6%29%28328%29%2B%28-4%29%28-568%29%3D304%20" alt="LaTeX: \displaystyle a_{7}=(-6)(328)+(-4)(-568)=304 " data-equation-content=" \displaystyle a_{7}=(-6)(328)+(-4)(-568)=304 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{8}=(-6)(-568)+(-4)(304)=2192 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B8%7D%3D%28-6%29%28-568%29%2B%28-4%29%28304%29%3D2192%20" alt="LaTeX: \displaystyle a_{8}=(-6)(-568)+(-4)(304)=2192 " data-equation-content=" \displaystyle a_{8}=(-6)(-568)+(-4)(304)=2192 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{9}=(-6)(304)+(-4)(2192)=-10592 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B9%7D%3D%28-6%29%28304%29%2B%28-4%29%282192%29%3D-10592%20" alt="LaTeX: \displaystyle a_{9}=(-6)(304)+(-4)(2192)=-10592 " data-equation-content=" \displaystyle a_{9}=(-6)(304)+(-4)(2192)=-10592 " /> . <br>
</p> </p>