Question

A theater has 30 rows of seats. There are 22 seats in the first row, 26 in the second row, 30 in the third row, etc. How many people will the theater hold ?

Answer 1

Arithmetic Sequence

rows ---------32-n

first term ------------26-----------a

d---------------------------4

Sn = n/2( 2a+(n-1)d)

=32/2 (2*26+(31)4)

=16(52+124)

=16(176)

=2816 seats

Answer 2

Total rows of seats, n = 30 rows of seats

First row, A1 = 22 seats

Second row, A2 = 26 seats

Third row, A3 = 30 seats

d = A3 - A2 = A2 - A1 = 4

then,

Sn = n/2 (2A1 + (n - 1)d)

Sn = 30/2 (2*22 + (30 - 1)4)

Sn = 15(44 + 116)

Sn = 2400 people