Question

Determine the seating capacity of an auditorium with 15 rows of seats if there are 25 seats in the first row, 29 seats in the second row, 33 seats in the third row, 37 seats in the forth row, and so on

Answer 1

The seating capacity of the auditorium is found by calculating the sum of an arithmetic series, which comes out to be 795 seats.

Step-by-step explanation:

The student is asking how to calculate the seating capacity of an auditorium with 15 rows, where the number of seats in each row follows a pattern that increases by 4 seats per row. To find the seating capacity, we can use the formula for the sum of an arithmetic series, because the number of seats forms such a series. The first row has 25 seats and each subsequent row has 4 more seats than the previous one.

This gives us an arithmetic series with the first term a1 = 25 and a common difference d = 4. Since there are 15 rows, we can determine the last term, a15, as follows: a15 = a1 + (15-1) × d = 25 + 14 × 4 = 81. The sum of an arithmetic series is given by Sn = n/2 × (a1 + an), where n is the number of terms. Therefore, the total seating capacity is S15 = 15/2 × (25 + 81) which is S15 = 15/2 × 106 = 795. The seating capacity of the auditorium with the given pattern is 795 seats.

Answer 2

Step-by-step explanation:

15 rows adding 4 additional seats to each. Once at end add all seats in rows together for the final answer.

1-25

2-29

3-33

4-37

5-41

6-45

7-49

8-53

9-57

10-61

11-65

12-69

13-73

14-77

15-81

Add all togther. 25+29+33+37+41+45+49+53+57+61+65+69+73+77+81=795

So there are 795 seating capacity.