A small auditorium has 10 rows of seats. There are 12 seats in the row and 16 seats in the second row the number of seats in a r
ow continues to increase by 4 with each additional row. What is the total number of seats in the auditorium?
1 answer:
This problem can be solved through simple arithmetic
progression
Let
a1 = the first term of the sequence
a(n) = the nth term of the sequence
n = number of terms
d = common difference
Sn = sum of all terms
given
a1 = 12
a2 = 16
n = 10
d = 16 -12 = 4
@n = 10
a(n) = a1 + (n-1)d
a(10) = 12 + (9)4
a(10) = 48 seats
Sn = (n/2) * (a1 + a(10))
Sn = 5* (12 + 48)
Sn = 300 seats
Therefore the total number of seats is 300.
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