An auditorium has 30 rows of seats. It has 20 seats on the first row, 24 seats on the second row, 28 seats on the third row, and so on.

1. How many seats are there in the 20th row?
2. How many seats are there in the whole auditorium?

You have an arithmetic progression where

a = 20
d = 4

T20 = 20+19*4 = 96
S30 = 30/2(2*20+29*4) = 2340

To find the number of seats in each row, we can use the formula:

Number of seats on a row = 20 + (row number - 1) * 4

1. To find the number of seats in the 20th row, we substitute the row number into the formula:

Number of seats on the 20th row = 20 + (20 - 1) * 4
= 20 + 19 * 4
= 20 + 76
= 96

Therefore, there are 96 seats in the 20th row.

2. To find the number of seats in the whole auditorium, we need to sum up the number of seats in each row.

Number of seats in the whole auditorium = Number of seats on the first row + Number of seats on the second row + ... + Number of seats on the 30th row

To find the sum, we can use the formula for the sum of an arithmetic sequence:

Sum = (n/2) * (first term + last term)

where n represents the number of terms in the sequence.

In this case, the first term is 20, the last term is 20 + (30 - 1) * 4 = 20 + 29 * 4 = 20 + 116 = 136, and the number of terms is 30.

Number of seats in the whole auditorium = (30/2) * (20 + 136)
= 15 * 156
= 2340

Therefore, there are 2340 seats in the whole auditorium.

To find the number of seats in the 20th row, you can use the given pattern of seat numbers increasing by 4 seats each row.

1. To find the number of seats in the 20th row, you can use the formula:
Number of seats = 20th row seat number - 1st row seat number + 1
In this case, the first row has 20 seats.
So, the number of seats in the 20th row is:
20th row seat number = 20 seats x 4 + 20 seats = 80 + 20 = 100 seats

Therefore, there are 100 seats in the 20th row.

2. To find the number of seats in the whole auditorium, you can use the formula for arithmetic progression sum:
Sum of seats = (number of rows / 2) * (first row seat number + last row seat number)
We know there are 30 rows and the first row has 20 seats.
Let's find the last row seat number. Using the given pattern, each row increases by 4 seats, so we can find the last row seat number:
Last row seat number = 20 seats + (30 - 1) * 4 = 20 seats + 29 * 4 = 20 seats + 116 = 136 seats

Now we can calculate the sum of seats:
Sum of seats = (30 / 2) * (20 seats + 136 seats)
= 15 rows * 156 seats
= 2340 seats

Therefore, there are 2340 seats in the whole auditorium.