Arithmetic Series Question..?

Question

A clothing store has 300 sweaters. 20 were sold in the 1st week, 40 in the 2nd, 60 in the 3rd, etc. If this pattern continued, how many weeks did it take to sell all 300 sweaters?

Answer 1

The sum of an arithmetic series can be determined with the formula:

S = [2 * a1 + (n - 1) d] * n / 2

In your case, a1 = 20, and d = 20

So, you need to solve for n:

300 = [2 * 20 + (n - 1) * 20] * n / 2

300 = [40 + 20n - 20] * n / 2

300 = (20 + 20n) * n / 2

300 = 10n² + 10n

30 = n² + n

0 = n² + n - 30

0 = (n + 6)(n - 5)

You should be able to get your answer from here.

Or, you can use guess and check.
(Guess and check is probably simpler for this problem, but it might not be for other problems of this type.)

Answer 2

5 weeks. The next predicted weekly sales are 80 and 100. Since 120 are already sold, the sum is 300.