. A theater has 40 rows of seats, where the first row has 27 seats and each subsequent row has 3 more seats than the previous one. Find the total number of seats in the theater.

number of seats in theater = 1035Step-by-step explanation:Given in question asTotal number of rows of seat = 30first row contain seat = 20second row contain seat = 21 .. and so onThis is in arithmetic progression as 20 , 21 , 22 , 23 so onThen as number of terms N = 30 and first terms = a = 20so we have to find Tn th termsSo, Tn th terms = first term + ( N -1 ) × d               d= common difference i.e 1     Tn th terms = 20 + (30 - 1) × 1Thus, Tn th terms = 49i.e The number of seats in 30th row = 49Now again Total number of seats in theatersum of Nth terms = so                         =                            = 15 × 69 = 1035Hence, Total number of seats in theater = 1035      Answer