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In the theatre, the number of seats in every row is four more than the number of seats of the preceding row. If there are 30 seats in the first row, what is the total seating capacity of the theatre if there are 30 rows?

 Feb 1, 2021
 #1
avatar+18 
+2

2640

 Feb 1, 2021
 #2
avatar+536 
+2

Row 1 has 30 seats, row 2 has 34, and so on.

The rule is Row x has 30+4(x-1) seats.

So row 30 would have 30+4(29) or 146 seats.

The sum of Row 1 and 30 is the same as the sum of rows 2 and 29, 3 and 28, and so on.

There are 15 pairs

146+30=176

176*15=2640.

 Feb 1, 2021
 #3
avatar+120287 
+1

Seats in first row =  30

 

Seats  in the last row = 30  + (30-1) (4)  =   30 + 29 (4)  =   146

 

Total  number of  seats  = 

 

(first row number  +  last row number )  (no. of rows  / 2)  =

 

(30  + 146)  ( 30  / 2)  =

 

(176) ( 15)   =

 

2640

 

 

cool cool cool

 Feb 1, 2021

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