kasiviv002 said:A Clothing store ordered 3420 sweaters and sold 20 of them at $100 each in the first week. In the second week, the selling price was lowered by $2, and 40 sweaters were sold. In the third week, the selling price was lowered by another $2, and 60 sweaters were sold. If the pattern continued, a) how many weeks did it take to sell all the sweaters? b) what was the selling price in the final week?
kasiviv002 said:Each week the number of sweaters being sold increases by 20.
week 1 -20 sweaters
week 2- 40 sweaters and so on
This is an arithmetic series.
Sn= 2/n[2a + (n-1)d] <<<<<< That equation is wrong. It should be:
\(\displaystyle S_n \ = \ \frac{n}{2}\cdot [2a \ + \ (n-1)\cdot d]\)
I tried to use the arithmetic series formula by plugging in 3420 for for 'Sn', 20 for 'a' and 20 for 'd'
and im not sure how to solve for 'n' to get the number of weeks
kasiviv002 said:S[sub:12t4foe8]n[/sub:12t4foe8]= n/2[2a + (n-1)d]
3420=n/2[2(20) + (n-1)(20)]
6840=n[40 + (n-1)(20)]
6840=n[40 + 20n -20]
6840=n[20 + 20n]
6840=20n + 20n^2
n[sup:12t4foe8]2[/sup:12t4foe8] + n + 342 = 0 ? (n +19)(n-18) = 0 ? n = 18
im not sure how to solve for 'n' from here on
never mind, i got it... Thank you