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Questions: Algebra BusinessCalculus
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Use \(\displaystyle a_1=-4\) and \(\displaystyle a_2=-8\) and \(\displaystyle a_n=-7a_{n-1} +4a_{n-2}\) to find \(\displaystyle a_{5}\)
Finding the next term in the sequence gives \(\displaystyle a_3=(-7)(-4)+(4)(-8)=-4\)
\(\displaystyle a_{4}=(-7)(-8)+(4)(-4)=40\).
\(\displaystyle a_{5}=(-7)(-4)+(4)(40)=188\).
\begin{question}Use $a_1=-4$ and $a_2=-8$ and $a_n=-7a_{n-1} +4a_{n-2}$ to find $a_{5}$
\soln{9cm}{Finding the next term in the sequence gives $a_3=(-7)(-4)+(4)(-8)=-4$\newline
$a_{4}=(-7)(-8)+(4)(-4)=40$. \newline
$a_{5}=(-7)(-4)+(4)(40)=188$. \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=-4 " src="/equation_images/%20%5Cdisplaystyle%20a_1%3D-4%20" alt="LaTeX: \displaystyle a_1=-4 " data-equation-content=" \displaystyle a_1=-4 " /> 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=-7a_{n-1} +4a_{n-2} " src="/equation_images/%20%5Cdisplaystyle%20a_n%3D-7a_%7Bn-1%7D%20%2B4a_%7Bn-2%7D%20" alt="LaTeX: \displaystyle a_n=-7a_{n-1} +4a_{n-2} " data-equation-content=" \displaystyle a_n=-7a_{n-1} +4a_{n-2} " /> to find <img class="equation_image" title=" \displaystyle a_{5} " src="/equation_images/%20%5Cdisplaystyle%20a_%7B5%7D%20" alt="LaTeX: \displaystyle a_{5} " data-equation-content=" \displaystyle a_{5} " /> </p> </p><p> <p>Finding the next term in the sequence gives <img class="equation_image" title=" \displaystyle a_3=(-7)(-4)+(4)(-8)=-4 " src="/equation_images/%20%5Cdisplaystyle%20a_3%3D%28-7%29%28-4%29%2B%284%29%28-8%29%3D-4%20" alt="LaTeX: \displaystyle a_3=(-7)(-4)+(4)(-8)=-4 " data-equation-content=" \displaystyle a_3=(-7)(-4)+(4)(-8)=-4 " /> <br>
<img class="equation_image" title=" \displaystyle a_{4}=(-7)(-8)+(4)(-4)=40 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B4%7D%3D%28-7%29%28-8%29%2B%284%29%28-4%29%3D40%20" alt="LaTeX: \displaystyle a_{4}=(-7)(-8)+(4)(-4)=40 " data-equation-content=" \displaystyle a_{4}=(-7)(-8)+(4)(-4)=40 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{5}=(-7)(-4)+(4)(40)=188 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B5%7D%3D%28-7%29%28-4%29%2B%284%29%2840%29%3D188%20" alt="LaTeX: \displaystyle a_{5}=(-7)(-4)+(4)(40)=188 " data-equation-content=" \displaystyle a_{5}=(-7)(-4)+(4)(40)=188 " /> . <br>
</p> </p>