The front row of an auditorium has 28 sets. Each of the remaining rows has 3 more sets than the row in front of it. If the auditorium has 32 rows, how many sets does it have ?

Options

A. 1440
B. 2384
C. 2688
D. 2784

Answer

B

Explanation

This question requires you to find the sum of an arithmetic sequence. One formula you can use to find the sum is `S_(n)=(n)/(2)(2a_(1)+(n-1)d)`, where n is the number of terms in the sequence, `a_(1)` is the first term, and d is the difference between one term and the next. Since there are 32 rows, and the number of seats in a row increases by 3 :
`S_(n)=(32)/(2)(2(28)+(32-1)3)=16(56+93)=2,384`