An auditorium has 30 seats in the first row 32 seats in the

An auditorium has 30 seats in the first row, 32 seats in the second row, 34 seats in the third row, and so on. If there are twenty rows in the auditorium, how many seats are there in the last row? How many seats are there in the auditorium?

Fill in the blanks:

There are ______ seats in the last row.

There are ______ in the auditorium.

Solution

30 seats in the first row

a=30

32 seats in the second row

=>common difference d =32-30=2

nth term =a+(n-1)d

twenty rows in the auditorium

number of seats in the last row=a+(20-1)d

=30+(19)*2

=30+38

=68 seats

total number of seats =(n/2)[2a+(n-1)d]

=(20/2)[2*30 +(20-1)*2]

=20[30+19]

=980 seats