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Questions: Algebra BusinessCalculus
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Use \(\displaystyle a_1=5\) and \(\displaystyle a_2=-8\) and \(\displaystyle a_n=3a_{n-1} +7a_{n-2}\) to find \(\displaystyle a_{6}\)
Finding the next term in the sequence gives \(\displaystyle a_3=(3)(5)+(7)(-8)=-41\)
\(\displaystyle a_{4}=(3)(-8)+(7)(-41)=-311\).
\(\displaystyle a_{5}=(3)(-41)+(7)(-311)=-2300\).
\(\displaystyle a_{6}=(3)(-311)+(7)(-2300)=-17033\).
\begin{question}Use $a_1=5$ and $a_2=-8$ and $a_n=3a_{n-1} +7a_{n-2}$ to find $a_{6}$
\soln{9cm}{Finding the next term in the sequence gives $a_3=(3)(5)+(7)(-8)=-41$\newline
$a_{4}=(3)(-8)+(7)(-41)=-311$. \newline
$a_{5}=(3)(-41)+(7)(-311)=-2300$. \newline
$a_{6}=(3)(-311)+(7)(-2300)=-17033$. \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=5 " src="/equation_images/%20%5Cdisplaystyle%20a_1%3D5%20" alt="LaTeX: \displaystyle a_1=5 " data-equation-content=" \displaystyle a_1=5 " /> 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=3a_{n-1} +7a_{n-2} " src="/equation_images/%20%5Cdisplaystyle%20a_n%3D3a_%7Bn-1%7D%20%2B7a_%7Bn-2%7D%20" alt="LaTeX: \displaystyle a_n=3a_{n-1} +7a_{n-2} " data-equation-content=" \displaystyle a_n=3a_{n-1} +7a_{n-2} " /> to find <img class="equation_image" title=" \displaystyle a_{6} " src="/equation_images/%20%5Cdisplaystyle%20a_%7B6%7D%20" alt="LaTeX: \displaystyle a_{6} " data-equation-content=" \displaystyle a_{6} " /> </p> </p><p> <p>Finding the next term in the sequence gives <img class="equation_image" title=" \displaystyle a_3=(3)(5)+(7)(-8)=-41 " src="/equation_images/%20%5Cdisplaystyle%20a_3%3D%283%29%285%29%2B%287%29%28-8%29%3D-41%20" alt="LaTeX: \displaystyle a_3=(3)(5)+(7)(-8)=-41 " data-equation-content=" \displaystyle a_3=(3)(5)+(7)(-8)=-41 " /> <br>
<img class="equation_image" title=" \displaystyle a_{4}=(3)(-8)+(7)(-41)=-311 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B4%7D%3D%283%29%28-8%29%2B%287%29%28-41%29%3D-311%20" alt="LaTeX: \displaystyle a_{4}=(3)(-8)+(7)(-41)=-311 " data-equation-content=" \displaystyle a_{4}=(3)(-8)+(7)(-41)=-311 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{5}=(3)(-41)+(7)(-311)=-2300 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B5%7D%3D%283%29%28-41%29%2B%287%29%28-311%29%3D-2300%20" alt="LaTeX: \displaystyle a_{5}=(3)(-41)+(7)(-311)=-2300 " data-equation-content=" \displaystyle a_{5}=(3)(-41)+(7)(-311)=-2300 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{6}=(3)(-311)+(7)(-2300)=-17033 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B6%7D%3D%283%29%28-311%29%2B%287%29%28-2300%29%3D-17033%20" alt="LaTeX: \displaystyle a_{6}=(3)(-311)+(7)(-2300)=-17033 " data-equation-content=" \displaystyle a_{6}=(3)(-311)+(7)(-2300)=-17033 " /> . <br>
</p> </p>