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Neporo4naja [7]
3 years ago
14

why does it always increase by one? will report if use this just for points and will give 200 more points if correct I need this

asap

Mathematics
1 answer:
Tpy6a [65]3 years ago
8 0

Answer:

REVENGE

Step-by-step explanation:

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to get the slope of a line all we need is two points off of it, so let's get two points from that table

\bf ~\hspace{4em}\downarrow ~\hspace{1.5em}\downarrow \\ \begin{array}{|ccccc|} \cline{1-5} x&0&1&2&3\\ \cline{1-5} y&-\frac{1}{3}&\frac{1}{3}&1&\frac{5}{3} \\ \cline{1-5} \end{array}\qquad \qquad (\stackrel{x_1}{1}~,~\stackrel{y_1}{\frac{1}{3}})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{\frac{5}{3}})

\bf \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{\frac{5}{3}}-\stackrel{y1}{\frac{1}{3}}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}}\implies \cfrac{~~\frac{4}{3}~~}{2}\implies \cfrac{~~\frac{4}{3}~~}{\frac{2}{1}}\implies \cfrac{\stackrel{2}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{3}\cdot \cfrac{1}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{2}{3}

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\bf 8~~,~~\stackrel{8-2}{6}~~,~~\stackrel{6-2}{4}~~,~~\stackrel{4-2}{2}~~,~~\stackrel{2-2}{0}


so, as you can see, the common difference is then -2, and the first term is clearly 8, thus


\bf n^{th}\textit{ term of an arithmetic sequence}\\\\a_n=a_1+(n-1)d\qquad\begin{cases}n=n^{th}\ term\\a_1=\textit{first term's value}\\d=\textit{common difference}\\[-0.5em]\hrulefill\\a_1=8\\d=-2\\n=14\end{cases}\\\\\\a_{14}=8+(14-1)(-2)\implies a_{14}=8-26\implies a_{14}=-18

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4 years ago
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