Question

Determine the seating capacity of an auditorium with 35 rows of seats if there are 20 seats in the first row, 23 seats in the second row, 26 seats in the third row, 29 seats in the forth row, and so on.

Answer 1

2485

Explanation:

The number of seats in row n is given by the explicit formula for an arithmetic sequence:

an = a1 +d(n -1)

an = 20 +3(n -1)

The middle row is row 18, so has ...

a18 = 20 + 3(18 -1) = 71 . . . . seats

The total number of seats is the product of the number of rows and the number of seats in the middle row:

capacity = (71)(35) = 2485

The seating capacity is 2485.