SOLUTION: A theater has 40 rows with 30 seats in the first row, 33 in the second row, 36 in the third row, and so forth. How many seats are in the theater? a.) 3600 b.) 7080 c.) 7200 d.)

Algebra ->  Sequences-and-series -> SOLUTION: A theater has 40 rows with 30 seats in the first row, 33 in the second row, 36 in the third row, and so forth. How many seats are in the theater? a.) 3600 b.) 7080 c.) 7200 d.)      Log On


   



Question 1059615: A theater has 40 rows with 30 seats in the first row, 33 in the second row, 36 in the third row, and so forth. How many seats are in the theater?
a.) 3600
b.) 7080
c.) 7200
d.) 3540

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
So the nth row has,
X%5Bn%5D=30%2B%28n-1%29%2A3=27%2B3n seats
The sum of the 40 rows is,
S%5B40%5D=%2840%2F2%29%28X%5B1%5D%2BX%5B40%5D%29
S%5B40%5D=20%2830%2B147%29
S%5B40%5D=3540