3
$\begingroup$

{...,−8,−3,2,7,12,17,...}

Hello, I need help writing this set in a set-builder notation. How do I find the steps?

Thank you

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    What do you mean by "set-builder" notation? – 2017-02-24
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    @TheCount What is says on the tin: a [notation for building sets](https://en.wikipedia.org/wiki/Set-builder_notation). – 2017-02-24
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    @GrahamKemp Would you believe I'm almost done an MS in math and never heard that term before? As soon as I clicked I knew exactly what it was, but I never heard it given a name. The things you learn. Thanks! – 2017-02-24

1 Answers 1

2

$$ A = \{5k+2: k\in\mathbb{Z}\} $$

To determine this, we first look at what is changing between each successive element in your set. Since we progress $2\to7\to12$, we start to suspect the pattern is $+5$. If we look at the negative values, it seems as though this is true! This means we want the formula for our set to have $5k$ in it, since adding $5$ to $5k$ is $5k + 5 = 5(k+1)$.

So now, what should happen if $k=0$? Note that the smallest positive element is $2$, so maybe we try $5k+2$ as our formula. Since if $k=0$ then our formula $5k+2=2$, this checks out!

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    ah thank you so much, ill write this in my notes – 2017-02-24