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Questions: Algebra BusinessCalculus
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Use \(\displaystyle a_1=1\) and \(\displaystyle a_2=9\) and \(\displaystyle a_n=-4a_{n-1} +8a_{n-2}\) to find \(\displaystyle a_{8}\)
Finding the next term in the sequence gives \(\displaystyle a_3=(-4)(1)+(8)(9)=68\)
\(\displaystyle a_{4}=(-4)(9)+(8)(68)=508\).
\(\displaystyle a_{5}=(-4)(68)+(8)(508)=3792\).
\(\displaystyle a_{6}=(-4)(508)+(8)(3792)=28304\).
\(\displaystyle a_{7}=(-4)(3792)+(8)(28304)=211264\).
\(\displaystyle a_{8}=(-4)(28304)+(8)(211264)=1576896\).
\begin{question}Use $a_1=1$ and $a_2=9$ and $a_n=-4a_{n-1} +8a_{n-2}$ to find $a_{8}$
\soln{9cm}{Finding the next term in the sequence gives $a_3=(-4)(1)+(8)(9)=68$\newline
$a_{4}=(-4)(9)+(8)(68)=508$. \newline
$a_{5}=(-4)(68)+(8)(508)=3792$. \newline
$a_{6}=(-4)(508)+(8)(3792)=28304$. \newline
$a_{7}=(-4)(3792)+(8)(28304)=211264$. \newline
$a_{8}=(-4)(28304)+(8)(211264)=1576896$. \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=1 " src="/equation_images/%20%5Cdisplaystyle%20a_1%3D1%20" alt="LaTeX: \displaystyle a_1=1 " data-equation-content=" \displaystyle a_1=1 " /> and <img class="equation_image" title=" \displaystyle a_2=9 " src="/equation_images/%20%5Cdisplaystyle%20a_2%3D9%20" alt="LaTeX: \displaystyle a_2=9 " data-equation-content=" \displaystyle a_2=9 " /> and <img class="equation_image" title=" \displaystyle a_n=-4a_{n-1} +8a_{n-2} " src="/equation_images/%20%5Cdisplaystyle%20a_n%3D-4a_%7Bn-1%7D%20%2B8a_%7Bn-2%7D%20" alt="LaTeX: \displaystyle a_n=-4a_{n-1} +8a_{n-2} " data-equation-content=" \displaystyle a_n=-4a_{n-1} +8a_{n-2} " /> to find <img class="equation_image" title=" \displaystyle a_{8} " src="/equation_images/%20%5Cdisplaystyle%20a_%7B8%7D%20" alt="LaTeX: \displaystyle a_{8} " data-equation-content=" \displaystyle a_{8} " /> </p> </p><p> <p>Finding the next term in the sequence gives <img class="equation_image" title=" \displaystyle a_3=(-4)(1)+(8)(9)=68 " src="/equation_images/%20%5Cdisplaystyle%20a_3%3D%28-4%29%281%29%2B%288%29%289%29%3D68%20" alt="LaTeX: \displaystyle a_3=(-4)(1)+(8)(9)=68 " data-equation-content=" \displaystyle a_3=(-4)(1)+(8)(9)=68 " /> <br>
<img class="equation_image" title=" \displaystyle a_{4}=(-4)(9)+(8)(68)=508 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B4%7D%3D%28-4%29%289%29%2B%288%29%2868%29%3D508%20" alt="LaTeX: \displaystyle a_{4}=(-4)(9)+(8)(68)=508 " data-equation-content=" \displaystyle a_{4}=(-4)(9)+(8)(68)=508 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{5}=(-4)(68)+(8)(508)=3792 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B5%7D%3D%28-4%29%2868%29%2B%288%29%28508%29%3D3792%20" alt="LaTeX: \displaystyle a_{5}=(-4)(68)+(8)(508)=3792 " data-equation-content=" \displaystyle a_{5}=(-4)(68)+(8)(508)=3792 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{6}=(-4)(508)+(8)(3792)=28304 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B6%7D%3D%28-4%29%28508%29%2B%288%29%283792%29%3D28304%20" alt="LaTeX: \displaystyle a_{6}=(-4)(508)+(8)(3792)=28304 " data-equation-content=" \displaystyle a_{6}=(-4)(508)+(8)(3792)=28304 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{7}=(-4)(3792)+(8)(28304)=211264 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B7%7D%3D%28-4%29%283792%29%2B%288%29%2828304%29%3D211264%20" alt="LaTeX: \displaystyle a_{7}=(-4)(3792)+(8)(28304)=211264 " data-equation-content=" \displaystyle a_{7}=(-4)(3792)+(8)(28304)=211264 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{8}=(-4)(28304)+(8)(211264)=1576896 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B8%7D%3D%28-4%29%2828304%29%2B%288%29%28211264%29%3D1576896%20" alt="LaTeX: \displaystyle a_{8}=(-4)(28304)+(8)(211264)=1576896 " data-equation-content=" \displaystyle a_{8}=(-4)(28304)+(8)(211264)=1576896 " /> . <br>
</p> </p>