Question

Amazing news! Cher is not only still alive, but will be visiting Salt Lake as part of her "Sixth Decade Still Touring" tour. Unfortunately, this legendary diva's career has aged like cheap milk left in the school lockers over summer vacation. Sales are off to a poor start.

On the first day of ticket availability, the venue sells 133 tickets. Each subsequent day sells 11 fewer tickets than the day before. If this pattern continues, how many tickets will be sold total?

Answer 1

Answer: 870

Explanation:

The tickets will sell until there is a day when a non-positive number of tickets will be sold.

`\lfloor 133/11 \rfloor=12`, so this will be after 12 days.

Thus, we can interpret this as an arithmetic series with 12 terms, a first term of 133, and a common difference of -11.

The sum of this series is
`(12)/(2)[2(133)+(12-1)(-11)]=870`.