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Questions: Algebra BusinessCalculus
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Use \(\displaystyle a_1=-6\) and \(\displaystyle a_2=-4\) and \(\displaystyle a_n=5a_{n-1} +4a_{n-2}\) to find \(\displaystyle a_{7}\)
Finding the next term in the sequence gives \(\displaystyle a_3=(5)(-6)+(4)(-4)=-46\)
\(\displaystyle a_{4}=(5)(-4)+(4)(-46)=-204\).
\(\displaystyle a_{5}=(5)(-46)+(4)(-204)=-1046\).
\(\displaystyle a_{6}=(5)(-204)+(4)(-1046)=-5204\).
\(\displaystyle a_{7}=(5)(-1046)+(4)(-5204)=-26046\).
\begin{question}Use $a_1=-6$ and $a_2=-4$ and $a_n=5a_{n-1} +4a_{n-2}$ to find $a_{7}$
\soln{9cm}{Finding the next term in the sequence gives $a_3=(5)(-6)+(4)(-4)=-46$\newline
$a_{4}=(5)(-4)+(4)(-46)=-204$. \newline
$a_{5}=(5)(-46)+(4)(-204)=-1046$. \newline
$a_{6}=(5)(-204)+(4)(-1046)=-5204$. \newline
$a_{7}=(5)(-1046)+(4)(-5204)=-26046$. \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=-6 " src="/equation_images/%20%5Cdisplaystyle%20a_1%3D-6%20" alt="LaTeX: \displaystyle a_1=-6 " data-equation-content=" \displaystyle a_1=-6 " /> and <img class="equation_image" title=" \displaystyle a_2=-4 " src="/equation_images/%20%5Cdisplaystyle%20a_2%3D-4%20" alt="LaTeX: \displaystyle a_2=-4 " data-equation-content=" \displaystyle a_2=-4 " /> and <img class="equation_image" title=" \displaystyle a_n=5a_{n-1} +4a_{n-2} " src="/equation_images/%20%5Cdisplaystyle%20a_n%3D5a_%7Bn-1%7D%20%2B4a_%7Bn-2%7D%20" alt="LaTeX: \displaystyle a_n=5a_{n-1} +4a_{n-2} " data-equation-content=" \displaystyle a_n=5a_{n-1} +4a_{n-2} " /> to find <img class="equation_image" title=" \displaystyle a_{7} " src="/equation_images/%20%5Cdisplaystyle%20a_%7B7%7D%20" alt="LaTeX: \displaystyle a_{7} " data-equation-content=" \displaystyle a_{7} " /> </p> </p><p> <p>Finding the next term in the sequence gives <img class="equation_image" title=" \displaystyle a_3=(5)(-6)+(4)(-4)=-46 " src="/equation_images/%20%5Cdisplaystyle%20a_3%3D%285%29%28-6%29%2B%284%29%28-4%29%3D-46%20" alt="LaTeX: \displaystyle a_3=(5)(-6)+(4)(-4)=-46 " data-equation-content=" \displaystyle a_3=(5)(-6)+(4)(-4)=-46 " /> <br>
<img class="equation_image" title=" \displaystyle a_{4}=(5)(-4)+(4)(-46)=-204 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B4%7D%3D%285%29%28-4%29%2B%284%29%28-46%29%3D-204%20" alt="LaTeX: \displaystyle a_{4}=(5)(-4)+(4)(-46)=-204 " data-equation-content=" \displaystyle a_{4}=(5)(-4)+(4)(-46)=-204 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{5}=(5)(-46)+(4)(-204)=-1046 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B5%7D%3D%285%29%28-46%29%2B%284%29%28-204%29%3D-1046%20" alt="LaTeX: \displaystyle a_{5}=(5)(-46)+(4)(-204)=-1046 " data-equation-content=" \displaystyle a_{5}=(5)(-46)+(4)(-204)=-1046 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{6}=(5)(-204)+(4)(-1046)=-5204 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B6%7D%3D%285%29%28-204%29%2B%284%29%28-1046%29%3D-5204%20" alt="LaTeX: \displaystyle a_{6}=(5)(-204)+(4)(-1046)=-5204 " data-equation-content=" \displaystyle a_{6}=(5)(-204)+(4)(-1046)=-5204 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{7}=(5)(-1046)+(4)(-5204)=-26046 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B7%7D%3D%285%29%28-1046%29%2B%284%29%28-5204%29%3D-26046%20" alt="LaTeX: \displaystyle a_{7}=(5)(-1046)+(4)(-5204)=-26046 " data-equation-content=" \displaystyle a_{7}=(5)(-1046)+(4)(-5204)=-26046 " /> . <br>
</p> </p>