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Questions: Algebra BusinessCalculus
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Use \(\displaystyle a_1=2\) and \(\displaystyle a_2=5\) and \(\displaystyle a_n=-9a_{n-1} +9a_{n-2}\) to find \(\displaystyle a_{8}\)
Finding the next term in the sequence gives \(\displaystyle a_3=(-9)(2)+(9)(5)=27\)
\(\displaystyle a_{4}=(-9)(5)+(9)(27)=198\).
\(\displaystyle a_{5}=(-9)(27)+(9)(198)=1539\).
\(\displaystyle a_{6}=(-9)(198)+(9)(1539)=12069\).
\(\displaystyle a_{7}=(-9)(1539)+(9)(12069)=94770\).
\(\displaystyle a_{8}=(-9)(12069)+(9)(94770)=744309\).
\begin{question}Use $a_1=2$ and $a_2=5$ and $a_n=-9a_{n-1} +9a_{n-2}$ to find $a_{8}$
\soln{9cm}{Finding the next term in the sequence gives $a_3=(-9)(2)+(9)(5)=27$\newline
$a_{4}=(-9)(5)+(9)(27)=198$. \newline
$a_{5}=(-9)(27)+(9)(198)=1539$. \newline
$a_{6}=(-9)(198)+(9)(1539)=12069$. \newline
$a_{7}=(-9)(1539)+(9)(12069)=94770$. \newline
$a_{8}=(-9)(12069)+(9)(94770)=744309$. \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=2 " src="/equation_images/%20%5Cdisplaystyle%20a_1%3D2%20" alt="LaTeX: \displaystyle a_1=2 " data-equation-content=" \displaystyle a_1=2 " /> and <img class="equation_image" title=" \displaystyle a_2=5 " src="/equation_images/%20%5Cdisplaystyle%20a_2%3D5%20" alt="LaTeX: \displaystyle a_2=5 " data-equation-content=" \displaystyle a_2=5 " /> and <img class="equation_image" title=" \displaystyle a_n=-9a_{n-1} +9a_{n-2} " src="/equation_images/%20%5Cdisplaystyle%20a_n%3D-9a_%7Bn-1%7D%20%2B9a_%7Bn-2%7D%20" alt="LaTeX: \displaystyle a_n=-9a_{n-1} +9a_{n-2} " data-equation-content=" \displaystyle a_n=-9a_{n-1} +9a_{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=(-9)(2)+(9)(5)=27 " src="/equation_images/%20%5Cdisplaystyle%20a_3%3D%28-9%29%282%29%2B%289%29%285%29%3D27%20" alt="LaTeX: \displaystyle a_3=(-9)(2)+(9)(5)=27 " data-equation-content=" \displaystyle a_3=(-9)(2)+(9)(5)=27 " /> <br>
<img class="equation_image" title=" \displaystyle a_{4}=(-9)(5)+(9)(27)=198 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B4%7D%3D%28-9%29%285%29%2B%289%29%2827%29%3D198%20" alt="LaTeX: \displaystyle a_{4}=(-9)(5)+(9)(27)=198 " data-equation-content=" \displaystyle a_{4}=(-9)(5)+(9)(27)=198 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{5}=(-9)(27)+(9)(198)=1539 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B5%7D%3D%28-9%29%2827%29%2B%289%29%28198%29%3D1539%20" alt="LaTeX: \displaystyle a_{5}=(-9)(27)+(9)(198)=1539 " data-equation-content=" \displaystyle a_{5}=(-9)(27)+(9)(198)=1539 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{6}=(-9)(198)+(9)(1539)=12069 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B6%7D%3D%28-9%29%28198%29%2B%289%29%281539%29%3D12069%20" alt="LaTeX: \displaystyle a_{6}=(-9)(198)+(9)(1539)=12069 " data-equation-content=" \displaystyle a_{6}=(-9)(198)+(9)(1539)=12069 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{7}=(-9)(1539)+(9)(12069)=94770 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B7%7D%3D%28-9%29%281539%29%2B%289%29%2812069%29%3D94770%20" alt="LaTeX: \displaystyle a_{7}=(-9)(1539)+(9)(12069)=94770 " data-equation-content=" \displaystyle a_{7}=(-9)(1539)+(9)(12069)=94770 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{8}=(-9)(12069)+(9)(94770)=744309 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B8%7D%3D%28-9%29%2812069%29%2B%289%29%2894770%29%3D744309%20" alt="LaTeX: \displaystyle a_{8}=(-9)(12069)+(9)(94770)=744309 " data-equation-content=" \displaystyle a_{8}=(-9)(12069)+(9)(94770)=744309 " /> . <br>
</p> </p>