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?

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

Hi again Svetlana! The first step I would do is find the lowest number of tickets that we will get to before we can no longer decrease by 11 again. This number would be 1 because 133 / 11 equals 12 remainder 1. So, our pattern in ascending order would be 1, 12, 23, 34, 45, 56, 67, 78, 89, 100, 111, 122, 133. We wish to find the sum of these numbers to determine the total number of tickets sold.

Notice that this is an arithmetic sequence. The sum of an arithmetic sequence is:

Sn = n ((a1 + an) / 2). n is the number of terms, a1 is the value of the first term, and an is the value of the last term in the sequence. In our case, n = 13, a1 = 1, and an = 133. We then have:

Sn = (13)((1 + 133) / 2) = (13)(134 / 2) = (13)(67) = 871 total tickets sold. Hope this helps.