An auditorium has 20 rows of seats.These are 20 seats in the first row,21 in the second row and 22 in the third row and so on.how many seats are there in all rows?
19(30) + 20= 590
To find the total number of seats in all rows of the auditorium, we can use the formula for the sum of an arithmetic series. In this case, the pattern is increasing by 1 seat per row.
The formula for the sum of an arithmetic series is:
Sn = (n/2)(2a + (n-1)d)
Where:
Sn is the sum of the first n terms of the series
n is the number of terms in the series
a is the first term in the series
d is the common difference between the terms in the series
In this case, n is equal to the number of rows (20 seats in the first row, 21 seats in the second row, 22 seats in the third row, and so on), a is the number of seats in the first row (20), and d is the common difference between the number of seats in each row (1).
Plugging in the values, we get:
Sn = (20/2)(2(20) + (20-1)(1))
= (10)(40 + 19)
= (10)(59)
= 590
Therefore, there are a total of 590 seats in all rows of the auditorium.