How would one put the following question in an equation?

A clothing store ordered 300 swearters and sold 20 of them at $100 each in the first week. In the second week, the selling price was lowered by $10, and 40 sweaters were sold. In the third week, the selling price was lowered by another $10, and 60 sweaters were sold. If the pattern continued,

a) how many week did it take to sell all the sweaters?

b) what was the selling price in the final week?

For a), I initially tried doing this:

0=300-20*(n-1)

=300-20n+20

n=15

but that didn't turn out right, so I'm starting to speculate a recusive aspect to the amount of sweaters sold? Same goes for part b). Any help here?

EDIT: I later tried this for a), it seems closer, but still wrong:

300=(n/2)*(20*(n-1))

600=n*(20n-20)

0=20n^2-20n-600

=20(n^2-n-30)

n=-5,6

The answer to a) is supposed to be 5, but this is as close as I can get.