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Questions: Algebra BusinessCalculus
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Use \(\displaystyle a_1=3\) and \(\displaystyle a_2=4\) and \(\displaystyle a_n=8a_{n-1} +1a_{n-2}\) to find \(\displaystyle a_{7}\)
Finding the next term in the sequence gives \(\displaystyle a_3=(8)(3)+(1)(4)=28\)
\(\displaystyle a_{4}=(8)(4)+(1)(28)=60\).
\(\displaystyle a_{5}=(8)(28)+(1)(60)=284\).
\(\displaystyle a_{6}=(8)(60)+(1)(284)=764\).
\(\displaystyle a_{7}=(8)(284)+(1)(764)=3036\).
\begin{question}Use $a_1=3$ and $a_2=4$ and $a_n=8a_{n-1} +1a_{n-2}$ to find $a_{7}$
\soln{9cm}{Finding the next term in the sequence gives $a_3=(8)(3)+(1)(4)=28$\newline
$a_{4}=(8)(4)+(1)(28)=60$. \newline
$a_{5}=(8)(28)+(1)(60)=284$. \newline
$a_{6}=(8)(60)+(1)(284)=764$. \newline
$a_{7}=(8)(284)+(1)(764)=3036$. \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=4 " src="/equation_images/%20%5Cdisplaystyle%20a_2%3D4%20" alt="LaTeX: \displaystyle a_2=4 " data-equation-content=" \displaystyle a_2=4 " /> and <img class="equation_image" title=" \displaystyle a_n=8a_{n-1} +1a_{n-2} " src="/equation_images/%20%5Cdisplaystyle%20a_n%3D8a_%7Bn-1%7D%20%2B1a_%7Bn-2%7D%20" alt="LaTeX: \displaystyle a_n=8a_{n-1} +1a_{n-2} " data-equation-content=" \displaystyle a_n=8a_{n-1} +1a_{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=(8)(3)+(1)(4)=28 " src="/equation_images/%20%5Cdisplaystyle%20a_3%3D%288%29%283%29%2B%281%29%284%29%3D28%20" alt="LaTeX: \displaystyle a_3=(8)(3)+(1)(4)=28 " data-equation-content=" \displaystyle a_3=(8)(3)+(1)(4)=28 " /> <br>
<img class="equation_image" title=" \displaystyle a_{4}=(8)(4)+(1)(28)=60 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B4%7D%3D%288%29%284%29%2B%281%29%2828%29%3D60%20" alt="LaTeX: \displaystyle a_{4}=(8)(4)+(1)(28)=60 " data-equation-content=" \displaystyle a_{4}=(8)(4)+(1)(28)=60 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{5}=(8)(28)+(1)(60)=284 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B5%7D%3D%288%29%2828%29%2B%281%29%2860%29%3D284%20" alt="LaTeX: \displaystyle a_{5}=(8)(28)+(1)(60)=284 " data-equation-content=" \displaystyle a_{5}=(8)(28)+(1)(60)=284 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{6}=(8)(60)+(1)(284)=764 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B6%7D%3D%288%29%2860%29%2B%281%29%28284%29%3D764%20" alt="LaTeX: \displaystyle a_{6}=(8)(60)+(1)(284)=764 " data-equation-content=" \displaystyle a_{6}=(8)(60)+(1)(284)=764 " /> . <br>
<img class="equation_image" title=" \displaystyle a_{7}=(8)(284)+(1)(764)=3036 " src="/equation_images/%20%5Cdisplaystyle%20a_%7B7%7D%3D%288%29%28284%29%2B%281%29%28764%29%3D3036%20" alt="LaTeX: \displaystyle a_{7}=(8)(284)+(1)(764)=3036 " data-equation-content=" \displaystyle a_{7}=(8)(284)+(1)(764)=3036 " /> . <br>
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