00:03
We have a theater that has 35 rows in.
00:09
In the first row, there are 20 seats, and each subsequent row has three more seats than the row in front of it.
00:18
So row 2 is going to have 23 seats.
00:20
Row 3 has 26 seats.
00:23
You keep adding three seats to each subsequent row.
00:26
R row 4 has 29 seats.
00:28
Row 35 is going to have a whole bunch of seats.
00:33
We need to find out the total number of seats.
00:37
The entire theater in all 35 rows.
00:44
Well, we're going to start by writing this 20 as 17 plus 3 times 1.
00:54
3 times 1 is 3 plus 17 is 20.
00:57
We're going to write 23 as 17 plus 3 times 2.
01:02
3 times 2 is 6 plus 17 is 23.
01:05
26 seats we're going to represent that as 17 plus 3 times 3.
01:10
Three times three is nine plus 17 is 26.
01:15
29 seats will be 17 plus three times four.
01:21
Three times four, 12 plus 17 is 29.
01:26
We need to find a total number of seats in the entire theater, but we can, using this little mini formula, we can actually find a number of seats in row 35.
01:36
Row 35 obviously is going to have 17 plus three times, well the one is the same as the row number two row two three row three or row four so three times four for row four three times 35 for row 35 so this does represent a number of seats in row 35 but now we need a total number of seats in the theater now to add a total number of seats in the entire theater we need to add up the number of seats in each well, you can see each one of these rows has a 17.
02:18
So there's 35 rows, each of them with a 17.
02:22
So you know we're going to have 17 times 35.
02:29
Plus, then we have to add up all of these.
02:36
3 times 1, 3 times 2, plus 3 times 3, 3 times 4...