An ancient Greek theater has 15 seats in the first row. Each row behind the first row has 2 [6 points] additional seats than the row before. If there are 30 rows, how many seats are in the theater?

Answer 1

According to the data given in the question there are 15 seats in the first row and there are two more seats in the all other rows and the total number of rows is 30. Means that in the first row there are 15 seats while in the second row there are 15+2=17 seats while in the third there are two more, means that 17+2=19 seats and so on, till the 30th row has 73 seats. We came to know this by the shape of the ancient theatres. As the outermost row is the largest and the innermost row is the smallest. So, by keeping on adding two seats in each of the rows starting from the innermost row, the circles get bigger and that shape is attained. So after counting the numbers of seats in all the 30 rows present in the theatre, the total number of seats are 1320.