PATTERNS, FUR1 2013 VCAA 6 MC

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?

A. `5`

B. `6`

C. `8`

D. `34`

D. `57`

Show Answers Only

`C`

Show Worked Solution

`200+250+300+…`

`text(AP where)\ \ \ a`	`=200`
`d`	`=250-200=50`

`text(Find)\ n,\ text(when)\ S_n=3000`

`n^2+7n-120`	`=0`
`(n-8)(n+15)`	`=0`

`:. n=8,\ \ \ (n>0)`

`=> C`