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Alex787 [66]
3 years ago
10

What is the common difference for the sequence shown below?

Mathematics
1 answer:
Nezavi [6.7K]3 years ago
5 0

we can always find the slope of any line by simply using two points on the line, say let's  use (3,4) and (-1,2)

\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{2-4}{-1-3}\implies \cfrac{-2}{-4}\implies \stackrel{\stackrel{\textit{common difference}}{\downarrow }}{\cfrac{1}{2}}

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Since <em>N</em>/2 leaves a remainder, <em>N</em> must be odd and ends with 1, 3, 5, 7, or 9.

<em>N</em>/5 also leaves a remainder, so <em>N</em> is not divisible by 5, so it does not end in 5.

The only correct choice is then 9, since

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9 = 1•5 + <u>4</u> and 9 = 4•2 + <u>1</u>

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Alternatively, the given information is equivalent to saying

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