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A theater has 30 seats in the first row, 33 seats in the second row, 36 seats in the third row, and so on in the same increasing pattern. If the theater has 15 rows of seats, how many seats are in the theater?

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30+33+36+39+42+45+48+51+54+57+60+63+66+69+72

Which equals up to 765 seats

Answer:

Number of seats in theater=765

Step-by-step explanation:

A theater has 30 seats in the first row

33 seats in the second row

36 seats in the third row

and so on

the pattern of seats will be

30  33  36  39  42  45  48  51  54  57  60  63  66  69  72

The upper pattern is in arithmetic progression having n=15 terms

sum of arithmetic progression is

   n(first term+last term)/2

hence, number of seats in theater=  15(30+72)/2

                                                       = 765

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