Question

a large Multiplex movie house has many theaters. the largest theater has 40 rows. there are 11 seats in the first row each row has three seats more than the previous row how many total seats are in this theater

Answer 1

The seats represent an arithmetic sequence

the first term is 11 and the common difference = 3

let the first term = a and the common difference = d and the general term = x

the general term = x = a + d(n-1)

at the the row number 40,

the number of seats at row 40 = 11 + 3 (40 - 1) = 128

To find the total seats, we need to find the number of seats at the first and the last rows

the sum of the arithmetic sequence = n/2 * (first term + last term)

so, the number of seats = (40/2) * ( 11 + 128 ) = 20 * 139 = 2780 seats

total seats = 2780