# 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?

Jun 24, 2018

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

#### Explanation:

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 $\left({x}_{0} + r\right) + r = {x}_{0} + 2 r$. Remember the rule: always add $r$ to the previous term to get the next.

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

$y = x + r , \setminus q \quad z = y + r$

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 $z$:

$z = \textcolor{red}{y} + r = \textcolor{red}{\left(x + r\right)} + r = x + 2 r$

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