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Questions: Algebra BusinessCalculus
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Use \(\displaystyle a_1=3\) and \(\displaystyle a_2=6\) and \(\displaystyle a_n=2a_{n-1} -2a_{n-2}\) to find \(\displaystyle a_{8}\)
Finding the next term in the sequence gives \(\displaystyle a_3=(2)(3)+(-2)(6)=-6\)
\(\displaystyle a_{4}=(2)(6)+(-2)(-6)=24\).
\(\displaystyle a_{5}=(2)(-6)+(-2)(24)=-60\).
\(\displaystyle a_{6}=(2)(24)+(-2)(-60)=168\).
\(\displaystyle a_{7}=(2)(-60)+(-2)(168)=-456\).
\(\displaystyle a_{8}=(2)(168)+(-2)(-456)=1248\).
\begin{question}Use $a_1=3$ and $a_2=6$ and $a_n=2a_{n-1} -2a_{n-2}$ to find $a_{8}$
\soln{9cm}{Finding the next term in the sequence gives $a_3=(2)(3)+(-2)(6)=-6$\newline
$a_{4}=(2)(6)+(-2)(-6)=24$. \newline
$a_{5}=(2)(-6)+(-2)(24)=-60$. \newline
$a_{6}=(2)(24)+(-2)(-60)=168$. \newline
$a_{7}=(2)(-60)+(-2)(168)=-456$. \newline
$a_{8}=(2)(168)+(-2)(-456)=1248$. \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=6 " src="/equation_images/%20%5Cdisplaystyle%20a_2%3D6%20" alt="LaTeX: \displaystyle a_2=6 " data-equation-content=" \displaystyle a_2=6 " /> and <img class="equation_image" title=" \displaystyle a_n=2a_{n-1} -2a_{n-2} " src="/equation_images/%20%5Cdisplaystyle%20a_n%3D2a_%7Bn-1%7D%20-2a_%7Bn-2%7D%20" alt="LaTeX: \displaystyle a_n=2a_{n-1} -2a_{n-2} " data-equation-content=" \displaystyle a_n=2a_{n-1} -2a_{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=(2)(3)+(-2)(6)=-6 " src="/equation_images/%20%5Cdisplaystyle%20a_3%3D%282%29%283%29%2B%28-2%29%286%29%3D-6%20" alt="LaTeX: \displaystyle a_3=(2)(3)+(-2)(6)=-6 " data-equation-content=" \displaystyle a_3=(2)(3)+(-2)(6)=-6 " /> <br>
<img class="equation_image" title=" \displaystyle a_{4}=(2)(6)+(-2)(-6)=24 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B4%7D%3D%282%29%286%29%2B%28-2%29%28-6%29%3D24%20" alt="LaTeX: \displaystyle a_{4}=(2)(6)+(-2)(-6)=24 " data-equation-content=" \displaystyle a_{4}=(2)(6)+(-2)(-6)=24 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{5}=(2)(-6)+(-2)(24)=-60 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B5%7D%3D%282%29%28-6%29%2B%28-2%29%2824%29%3D-60%20" alt="LaTeX: \displaystyle a_{5}=(2)(-6)+(-2)(24)=-60 " data-equation-content=" \displaystyle a_{5}=(2)(-6)+(-2)(24)=-60 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{6}=(2)(24)+(-2)(-60)=168 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B6%7D%3D%282%29%2824%29%2B%28-2%29%28-60%29%3D168%20" alt="LaTeX: \displaystyle a_{6}=(2)(24)+(-2)(-60)=168 " data-equation-content=" \displaystyle a_{6}=(2)(24)+(-2)(-60)=168 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{7}=(2)(-60)+(-2)(168)=-456 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B7%7D%3D%282%29%28-60%29%2B%28-2%29%28168%29%3D-456%20" alt="LaTeX: \displaystyle a_{7}=(2)(-60)+(-2)(168)=-456 " data-equation-content=" \displaystyle a_{7}=(2)(-60)+(-2)(168)=-456 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{8}=(2)(168)+(-2)(-456)=1248 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B8%7D%3D%282%29%28168%29%2B%28-2%29%28-456%29%3D1248%20" alt="LaTeX: \displaystyle a_{8}=(2)(168)+(-2)(-456)=1248 " data-equation-content=" \displaystyle a_{8}=(2)(168)+(-2)(-456)=1248 " /> . <br>
</p> </p>