Answer:
The seating capacity of the auditorium is 2,340.
Step-by-step explanation:
This question relates to an Arithmetic Progression (AP).
An Arithmetic Progression (AP) is a sequence of numbers in which the differences of every two consecutive numbers or terms are constant or the same.
Therefore, the seating capacity can be calculated using the an arithmetic progression (AP) formula as follows:
Seating capacity = (n / 2) * (2a_1 + (n - 1)d) ...................... (1)
Where;
n = number of rows = 30
a_1 = Number seats in the first row = 20
d = Common difference = 24 - 20 = 28 - 24 = 4
Substituting the values into equation (1), we have:
Seating capacity = (30 / 2) * ((2 * 20) + ((30 - 1) * 4))
Seating capacity = 15 * (40 + (29 * 4))
Seating capacity = 15 * (40 + 116)
Seating capacity = 15 * 156
Seating capacity = 2,340
Therefore, the seating capacity of the auditorium is 2,340.
