How many days does it take for all of the tickets to be sold?

Question

Here is the question :

There are 3000 tickets available for a concert.

On the first day of ticket sales, 200 tickets are sold.

On the second day, 250 tickets are sold.

On the third day, 300 tickets are sold.

This pattern of ticket sales continues until all 3000 tickets are sold.

How many days does it take for all of the tickets to be sold?

I know you use the formula : n/2 ( 2a + ( n-1) ) x d but Im doing something wrong and can't find the correct answer...

Answer 1

Sn = n/2(a+L) where n=number of terms, a=1st term, L=last term, Sn = sum

3000 = (n/2)(200+550) = (n/2)(750

6000=n(750)

n = 6000/750 = 8 days to get 3000 tickets sold

200

+250 total 450 on day 2

+300 total 750 day 3

+350 total 1100 day 4

+400 total 1500 day 5

+450 total 1950 day 6

+500 total 2450 day 7

+550 total 3000 day 8

8 days to sell 3,000

200+250 + ...+ 500+ 550

subtract 200 from each term

50+100 + ...+ 300+ 350

divide each term by 50

1+2+ ...+ 6+7

sum them to get 7(8)/2 = 28

28x50 = 1400

add 200 for each term = 8x200 = 1600

1400+1600 = 3000

n(n-1)/2 =7(8)/2 = 28

50n(n+1)/2= 50(28) =1400

200n =200(8)= 1600

200n + 50n(n-1)/2 = 3000

solve for n to get 8

4n+n(n-1)/2 =60

7n +n^2 +n = 120

n^2 + 7n -120= 0

(n-8)(n+15) = 0

n = 8

sum of the arithmetic sequence is either Sn =(n/2)(a+L) or

an +d(n)(n-1)/2 = Sn

a=1st term, d= common difference, n=number of terms

200(8)+50(8)(7)/2 = 3000

1600+1400 = 3000

a=1st term

an +(a/4)n(n+1)/2 = 3000