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Questions: Algebra BusinessCalculus
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Use \(\displaystyle a_1=-8\) and \(\displaystyle a_2=4\) and \(\displaystyle a_n=9a_{n-1} -7a_{n-2}\) to find \(\displaystyle a_{5}\)
Finding the next term in the sequence gives \(\displaystyle a_3=(9)(-8)+(-7)(4)=-100\)
\(\displaystyle a_{4}=(9)(4)+(-7)(-100)=736\).
\(\displaystyle a_{5}=(9)(-100)+(-7)(736)=-6052\).
\begin{question}Use $a_1=-8$ and $a_2=4$ and $a_n=9a_{n-1} -7a_{n-2}$ to find $a_{5}$
\soln{9cm}{Finding the next term in the sequence gives $a_3=(9)(-8)+(-7)(4)=-100$\newline
$a_{4}=(9)(4)+(-7)(-100)=736$. \newline
$a_{5}=(9)(-100)+(-7)(736)=-6052$. \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=-8 " src="/equation_images/%20%5Cdisplaystyle%20a_1%3D-8%20" alt="LaTeX: \displaystyle a_1=-8 " data-equation-content=" \displaystyle a_1=-8 " /> and <img class="equation_image" title=" \displaystyle a_2=4 " src="/equation_images/%20%5Cdisplaystyle%20a_2%3D4%20" alt="LaTeX: \displaystyle a_2=4 " data-equation-content=" \displaystyle a_2=4 " /> and <img class="equation_image" title=" \displaystyle a_n=9a_{n-1} -7a_{n-2} " src="/equation_images/%20%5Cdisplaystyle%20a_n%3D9a_%7Bn-1%7D%20-7a_%7Bn-2%7D%20" alt="LaTeX: \displaystyle a_n=9a_{n-1} -7a_{n-2} " data-equation-content=" \displaystyle a_n=9a_{n-1} -7a_{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=(9)(-8)+(-7)(4)=-100 " src="/equation_images/%20%5Cdisplaystyle%20a_3%3D%289%29%28-8%29%2B%28-7%29%284%29%3D-100%20" alt="LaTeX: \displaystyle a_3=(9)(-8)+(-7)(4)=-100 " data-equation-content=" \displaystyle a_3=(9)(-8)+(-7)(4)=-100 " /> <br>
<img class="equation_image" title=" \displaystyle a_{4}=(9)(4)+(-7)(-100)=736 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B4%7D%3D%289%29%284%29%2B%28-7%29%28-100%29%3D736%20" alt="LaTeX: \displaystyle a_{4}=(9)(4)+(-7)(-100)=736 " data-equation-content=" \displaystyle a_{4}=(9)(4)+(-7)(-100)=736 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{5}=(9)(-100)+(-7)(736)=-6052 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B5%7D%3D%289%29%28-100%29%2B%28-7%29%28736%29%3D-6052%20" alt="LaTeX: \displaystyle a_{5}=(9)(-100)+(-7)(736)=-6052 " data-equation-content=" \displaystyle a_{5}=(9)(-100)+(-7)(736)=-6052 " /> . <br>
</p> </p>