Question

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?

Answer 1

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`.

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 `(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`