Question

There are 25 rows of seats in the high school auditorium with 20 seats in the first row, 21 seats in the second

row, 22 seats in the third row, and so on. How many total seats are in the auditorium?
OA) 800 seats
OB) 860 seats

Answer 1

A) 800 seats

Explanation:

Notice that an arithmetic sequence is formed with the number of seats. Since we're adding one seat each row, the last (25th) row will have 44 seats since the first row has 20 seats.

The sum of an arithmetic sequence is given by:

`S_n=n\left((a_1+a_n)/(2)\right)`, where
`n` is the number of terms,
`a_1` is the first term, and
`a_n` is the last term

Therefore, substituting
`a_1=20`,
`a_n=44`, and
`n=25`, we get:

`S_n=25((20+44)/(2)),\\s_n=25\cdot 32=\boxed{800}`