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Questions: Algebra BusinessCalculus
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Use \(\displaystyle a_1=3\) and \(\displaystyle a_2=-8\) and \(\displaystyle a_n=-4a_{n-1} -6a_{n-2}\) to find \(\displaystyle a_{9}\)
Finding the next term in the sequence gives \(\displaystyle a_3=(-4)(3)+(-6)(-8)=36\)
\(\displaystyle a_{4}=(-4)(-8)+(-6)(36)=-184\).
\(\displaystyle a_{5}=(-4)(36)+(-6)(-184)=960\).
\(\displaystyle a_{6}=(-4)(-184)+(-6)(960)=-5024\).
\(\displaystyle a_{7}=(-4)(960)+(-6)(-5024)=26304\).
\(\displaystyle a_{8}=(-4)(-5024)+(-6)(26304)=-137728\).
\(\displaystyle a_{9}=(-4)(26304)+(-6)(-137728)=721152\).
\begin{question}Use $a_1=3$ and $a_2=-8$ and $a_n=-4a_{n-1} -6a_{n-2}$ to find $a_{9}$
\soln{9cm}{Finding the next term in the sequence gives $a_3=(-4)(3)+(-6)(-8)=36$\newline
$a_{4}=(-4)(-8)+(-6)(36)=-184$. \newline
$a_{5}=(-4)(36)+(-6)(-184)=960$. \newline
$a_{6}=(-4)(-184)+(-6)(960)=-5024$. \newline
$a_{7}=(-4)(960)+(-6)(-5024)=26304$. \newline
$a_{8}=(-4)(-5024)+(-6)(26304)=-137728$. \newline
$a_{9}=(-4)(26304)+(-6)(-137728)=721152$. \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=3 " src="/equation_images/%20%5Cdisplaystyle%20a_1%3D3%20" alt="LaTeX: \displaystyle a_1=3 " data-equation-content=" \displaystyle a_1=3 " /> and <img class="equation_image" title=" \displaystyle a_2=-8 " src="/equation_images/%20%5Cdisplaystyle%20a_2%3D-8%20" alt="LaTeX: \displaystyle a_2=-8 " data-equation-content=" \displaystyle a_2=-8 " /> and <img class="equation_image" title=" \displaystyle a_n=-4a_{n-1} -6a_{n-2} " src="/equation_images/%20%5Cdisplaystyle%20a_n%3D-4a_%7Bn-1%7D%20-6a_%7Bn-2%7D%20" alt="LaTeX: \displaystyle a_n=-4a_{n-1} -6a_{n-2} " data-equation-content=" \displaystyle a_n=-4a_{n-1} -6a_{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=(-4)(3)+(-6)(-8)=36 " src="/equation_images/%20%5Cdisplaystyle%20a_3%3D%28-4%29%283%29%2B%28-6%29%28-8%29%3D36%20" alt="LaTeX: \displaystyle a_3=(-4)(3)+(-6)(-8)=36 " data-equation-content=" \displaystyle a_3=(-4)(3)+(-6)(-8)=36 " /> <br>
<img class="equation_image" title=" \displaystyle a_{4}=(-4)(-8)+(-6)(36)=-184 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B4%7D%3D%28-4%29%28-8%29%2B%28-6%29%2836%29%3D-184%20" alt="LaTeX: \displaystyle a_{4}=(-4)(-8)+(-6)(36)=-184 " data-equation-content=" \displaystyle a_{4}=(-4)(-8)+(-6)(36)=-184 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{5}=(-4)(36)+(-6)(-184)=960 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B5%7D%3D%28-4%29%2836%29%2B%28-6%29%28-184%29%3D960%20" alt="LaTeX: \displaystyle a_{5}=(-4)(36)+(-6)(-184)=960 " data-equation-content=" \displaystyle a_{5}=(-4)(36)+(-6)(-184)=960 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{6}=(-4)(-184)+(-6)(960)=-5024 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B6%7D%3D%28-4%29%28-184%29%2B%28-6%29%28960%29%3D-5024%20" alt="LaTeX: \displaystyle a_{6}=(-4)(-184)+(-6)(960)=-5024 " data-equation-content=" \displaystyle a_{6}=(-4)(-184)+(-6)(960)=-5024 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{7}=(-4)(960)+(-6)(-5024)=26304 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B7%7D%3D%28-4%29%28960%29%2B%28-6%29%28-5024%29%3D26304%20" alt="LaTeX: \displaystyle a_{7}=(-4)(960)+(-6)(-5024)=26304 " data-equation-content=" \displaystyle a_{7}=(-4)(960)+(-6)(-5024)=26304 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{8}=(-4)(-5024)+(-6)(26304)=-137728 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B8%7D%3D%28-4%29%28-5024%29%2B%28-6%29%2826304%29%3D-137728%20" alt="LaTeX: \displaystyle a_{8}=(-4)(-5024)+(-6)(26304)=-137728 " data-equation-content=" \displaystyle a_{8}=(-4)(-5024)+(-6)(26304)=-137728 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{9}=(-4)(26304)+(-6)(-137728)=721152 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B9%7D%3D%28-4%29%2826304%29%2B%28-6%29%28-137728%29%3D721152%20" alt="LaTeX: \displaystyle a_{9}=(-4)(26304)+(-6)(-137728)=721152 " data-equation-content=" \displaystyle a_{9}=(-4)(26304)+(-6)(-137728)=721152 " /> . <br>
</p> </p>