I dislike these questions because it's so easy to make a mistake.

The formula for an arithmetic series is

Where:

n = number of terms in the sequence that you are summing

a = first term in the sequence

d = the rate that the sequence is increasing or decreasing

In a), we can ignore prices. It's just the amount of sweaters that matters.

On the first week, 20 sweaters were sold. So a=20.

The amount of sweaters sold then increases by 20 to 40. So d=20.

And we want the sum of sweaters sold to be equal to 300

In this case, n=number of weeks

So the formula becomes:

By simplifying and manipulating, I got the correct answer of n=5 doing this, do you get the same result?

If yes, then work out what needs to be changed for b).

I can help further if necessary.