The numbers x, y, and z are the first three terms of an arithmetic sequence. How do you express z in terms of x and y?

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Answer 1 · 2018-06-24T09:29:40

Assuming $r$ is the constant difference between two consecutive terms, you express $z=y+r$ in terms of $y$ and $z=x+2r$ in terms of $x$ .

Each arithmetic sequence has a starting point $x_0$ and a particular number $r$ .

You get the next term by adding the constant number $n$ to the previous term.

So, the first term is $x_0$ , which is given.

The second term is $x_0+r$

The third term is again $(x_0+r)+r= x_0+2r$ . Remember the rule: always add $r$ to the previous term to get the next.

So, if the first term is $x$ , you have

$y=x+r,\qquad z=y+r$

This is how you express $z$ in terms of $y$ . If you want to express $z$ in terms of $x$ , plug the expression for $y$ in the expression for $z$ :

$z=color(red)(y)+r = color(red)((x+r))+r=x+2r$

and so $z=x+2r$ is how you express $z$ in terms of $x$