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Questions: Algebra BusinessCalculus
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Use \(\displaystyle a_1=-2\) and \(\displaystyle a_2=-1\) and \(\displaystyle a_n=4a_{n-1} +8a_{n-2}\) to find \(\displaystyle a_{5}\)
Finding the next term in the sequence gives \(\displaystyle a_3=(4)(-2)+(8)(-1)=-16\)
\(\displaystyle a_{4}=(4)(-1)+(8)(-16)=-132\).
\(\displaystyle a_{5}=(4)(-16)+(8)(-132)=-1120\).
\begin{question}Use $a_1=-2$ and $a_2=-1$ and $a_n=4a_{n-1} +8a_{n-2}$ to find $a_{5}$
\soln{9cm}{Finding the next term in the sequence gives $a_3=(4)(-2)+(8)(-1)=-16$\newline
$a_{4}=(4)(-1)+(8)(-16)=-132$. \newline
$a_{5}=(4)(-16)+(8)(-132)=-1120$. \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%3D-2%20" alt="LaTeX: \displaystyle a_1=-2 " data-equation-content=" \displaystyle a_1=-2 " /> and <img class="equation_image" title=" \displaystyle a_2=-1 " src="/equation_images/%20%5Cdisplaystyle%20a_2%3D-1%20" alt="LaTeX: \displaystyle a_2=-1 " data-equation-content=" \displaystyle a_2=-1 " /> and <img class="equation_image" title=" \displaystyle a_n=4a_{n-1} +8a_{n-2} " src="/equation_images/%20%5Cdisplaystyle%20a_n%3D4a_%7Bn-1%7D%20%2B8a_%7Bn-2%7D%20" alt="LaTeX: \displaystyle a_n=4a_{n-1} +8a_{n-2} " data-equation-content=" \displaystyle a_n=4a_{n-1} +8a_{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=(4)(-2)+(8)(-1)=-16 " src="/equation_images/%20%5Cdisplaystyle%20a_3%3D%284%29%28-2%29%2B%288%29%28-1%29%3D-16%20" alt="LaTeX: \displaystyle a_3=(4)(-2)+(8)(-1)=-16 " data-equation-content=" \displaystyle a_3=(4)(-2)+(8)(-1)=-16 " /> <br>
<img class="equation_image" title=" \displaystyle a_{4}=(4)(-1)+(8)(-16)=-132 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B4%7D%3D%284%29%28-1%29%2B%288%29%28-16%29%3D-132%20" alt="LaTeX: \displaystyle a_{4}=(4)(-1)+(8)(-16)=-132 " data-equation-content=" \displaystyle a_{4}=(4)(-1)+(8)(-16)=-132 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{5}=(4)(-16)+(8)(-132)=-1120 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B5%7D%3D%284%29%28-16%29%2B%288%29%28-132%29%3D-1120%20" alt="LaTeX: \displaystyle a_{5}=(4)(-16)+(8)(-132)=-1120 " data-equation-content=" \displaystyle a_{5}=(4)(-16)+(8)(-132)=-1120 " /> . <br>
</p> </p>