Question

Section 208 of nassau veterans Memorial Coliseum has 17 rows. The first row has 13 seats in it. If you add two seats to the previous row for each row in the section, how many seats are in row 15? How many seats total are there in the section?

Answer 1

Row 15 has 41 seats, and the entire section has 493 seats.

We can write the explicit formula for an arithmetic sequence to represent this, since we add 2 each time:

13+2(n-1)

Using 15 for n,
13+2(15-1) = 13+2(14) = 13+28 = 41

To find the total number of seats, we evaluate the sum
$\Sigma_{n=1}^{17} 13+2(n-1)$

Using technology to evaluate this sum, it is 493.