Question 1178677: The seating section in a theater has 19 seats in the first row, 21 seats in the second row, and so on, increasing by 2 seats each row for a total of 10 rows. How many seats are in the tenth row, and how many seats are there in the section?
Answer by greenestamps(13200)   (Show Source):
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The numbers of seats in the successive rows form an arithmetic sequence with first term 19 and common difference 2. The number of seats in row n is the number in the first row, plus the common difference (n-1) time:
t(n) = 19+2(n-1)
Number of seats in row 10: 19+2(10-1) = 19+18=37
The number of seats in rows 1-10 is the number of rows, multiplied by the average number of seats in each row. Since we have an arithmetic sequence, the average number of seats in all the rows is the average of the numbers of seats in the first and last rows.
# of rows: 10
average number of seats per row: (19+37)/2 = 28
total number of seats: 10(28) = 280
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