Arithmetic

Application

An auditorium has 20 seats on the first row, 24 seats on the second row, 28 seats on the third row, and so on. The auditorium has 30 rows of seats. How many seats are in the auditorium?

Step 1. Write an arithmetic sequence to represent the situation.

20, 24, 28, 32 â€¦

Step 2. Determine the general formula for the sequence.

Step 3. Determine a₁and a_n. For this situation, a₁= first row and a_n= last row.

and

Step 4. Determine the number of pairs in the sequence. In this situation there are 30 rows, so n = 30.

Step 5. To find the series, substitute and solve.

The auditorium has 2340 seats.