We have the following sequence $$ -a, -\dfrac{a}{b}, \dfrac{a}{b}, a$$

Determine the value of $b$ for which this is an arithmetic progression ($a \neq 0$)

I don't know how to do this. I've tried adding a variable and making a couple of equations:

* $-a + x = -\dfrac{a}{b}$
* $ -a + 2x = \dfrac{a}{b}$
* $-a + 3x = a$

But this doesn't seem to yield any logical answers. Just from looking at the sequence it seems that $b=2$ should be the answer, but I can't seem to get that result..